how to find experimental value in physics

#"Error" = "|experimental value - accepted value|"#

The difference is usually expressed as percent error .

#"% error" = "|experimental value - accepted value|"/"experimental value" × 100 %#

For example, suppose that you did an experiment to determine the boiling point of water and got a value of 99.3 °C.

Your experimental value is 99.3 °C.

The theoretical value is 100.0 °C.

The experimental error is #"|99.3 °C - 100.0 °C| = 0.7 °C"#

The percent error is #"|99.3 °C - 100.0 °C|"/"100.0 °C" = "0.7 °C"/"100.0 °C" × 100% = 0.7 %#

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Absolute and Relative Error and How to Calculate Them

Absolute, relative, and percent error are the most common experimental error calculations in science. Grouped together, they are types of approximation error. Basically, the premise is that no matter how carefully you measure something, you’ll always be off a bit due to the limitations of the measuring instrument. For example, you may be only able to measure to the nearest millimeter on a ruler or the nearest milliliter on a graduated cylinder. Here are the definitions, equations, and examples of how to use these types of error calculations.

Absolute Error

Absolute error is the magnitude (size) of the difference between a measured value and a true or exact value.

Absolute Error = |True Value – Measured Value|

Absolute Error Example: A measurement is 24.54 mm and the true or known value is 26.00 mm. Find the absolute error. Absolute Error = |26.00 mm – 25.54 mm|= 0.46 mm Note absolute error retains its units of measurement.

The vertical bars indicate absolute value . In other words, you drop any negative sign you may get. For this reason, it doesn’t actually matter whether you subtract the measured value from the true value or the other way around. You’ll see the formula written both ways in textbooks and both forms are correct.

What matters is that you interpret the error correctly. If you graph error bars, half of the error is higher than the measured value and half is lower. For example, if your error is 0.2 cm, it is the same as saying ±0.1 cm.

The absolute error tells you how big a difference there is between the measured and true values, but this information isn’t very helpful when you want to know if the measured value is close to the real value or not. For example, an absolute error of 0.1 grams is more significant if the true value is 1.4 grams than if the true value is 114 kilograms! This is where relative error and percent error help.

Relative Error

Relative error puts absolute error into perspective because it compares the size of absolute error to the size of the true value. Note that the units drop off in this calculation, so relative error is dimensionless (unitless).

Relative Error = |True Value – Measured Value| / True Value Relative Error = Absolute Error / True Value

Relative Error Example: A measurement is 53 and the true or known value is 55. Find the relative error. Relative Error = |55 – 53| / 55 = 0.034 Note this value maintains two significant digits.

Note: Relative error is undefined when the true value is zero . Also, relative error only makes sense when a measurement scale starts at a true zero. So, it makes sense for the Kelvin temperature scale, but not for Fahrenheit or Celsius!

Percent Error

Percent error is just relative error multiplied by 100%. It tells what percent of a measurement is questionable.

Percent Error = |True Value – Measured Value| / True Value x 100% Percent Error = Absolute Error / True Value x 100% Percent Error = Relative Error x 100%

Percent Error Example: A speedometer says a car is going 70 mph but its real speed is 72 mph. Find the percent error. Percent Error = |72 – 70| / 72 x 100% = 2.8%

Mean Absolute Error

Absolute error is fine if you’re only taking one measurement, but what about when you collect more data? Then, mean absolute error is useful. Mean absolute error or MAE is the sum of all the absolute errors divided by the number of errors (data points). In other words, it’s the average of the errors. Mean absolute error, like absolute error, retains its units.

Mean Absolute Error Example: You weigh yourself three times and get values of 126 lbs, 129 lbs, 127 lbs. Your true weight is 127 lbs. What is the mean absolute error of the measurements. Mean Absolute Error = [|126-127 lbs|+|129-127 lbs|+|127-127 lbs|]/3 = 1 lb

• Hazewinkel, Michiel, ed. (2001). “Theory of Errors.”  Encyclopedia of Mathematics . Springer Science+Business Media B.V. / Kluwer Academic Publishers. ISBN 978-1-55608-010-4.
• Helfrick, Albert D. (2005). Modern Electronic Instrumentation and Measurement Techniques . ISBN 81-297-0731-4.
• Steel, Robert G. D.; Torrie, James H. (1960).  Principles and Procedures of Statistics, With Special Reference to Biological Sciences . McGraw-Hill. 

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How to Calculate the Percent Error Formula

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We all make mistakes. Sometimes, if you play your cards right, they can become valuable learning opportunities. It's called "human error" for a reason; even the best of us leave a "t" uncrossed or an "i" undotted now and then. Such is life.

Before trying to correct a blooper , gaffe or snafu (did you know a thesaurus makes a great gift?), it's usually a good idea to find out what went wrong in the first place.

The size of the error is a key detail. How badly did you miss the mark? Was it a close shave or wildly off-base?

Picture a violinist in a philharmonic orchestra. On the night of a big concert, he misses an important cue and plays some notes too late. If he missed the cue by half a second, it might not be a huge deal. But if he missed it by half a minute , that's a different can of worms.

When there's a difference between the value you expected and the value you actually got — and you express that difference as a mathematical percentage — it's called a percent error or percentage error . Calculating percentage error involves comparing an expected value and an actual value to determine how far reality deviated from theoretical expectations.

Today, we're going to take the mystery out of reporting the percent error correctly and show you how to use it in real life.

What Is the Percent Error Formula?

The equation couldn't be much simpler. Here it is:

Percent Error = | Experimental Value – Actual Value | / Actual Value x 100%

The value you originally projected goes by many names, including exact value, accepted value, estimated value, theoretical value, approximate value or experimental value, depending on the context. For instance, a physics student calculating speed will refer to an accepted value based on the velocity formula , but the approximate or measured value of speed in her experiment may differ. In another scenario, a business owner may refer to an estimated value when forecasting revenue.

Similarly, there are multiple labels for your real-life result, including actual value, measured value, and exact or known value. No matter what you call it, the spirit behind the actual number itself remains the same.

Some people find written instructions more helpful than mathematical formulas. If you're one of them, no worries. Here's a step-by-step walkthrough for percent error calculation:

• Step One: Take the experimental value and subtract the actual value from it. This is called the relative error.
• Step Two: Take the absolute value of the number you arrived at in Step One (that's what those two vertical lines indicate). This new number is called the absolute error and ensures that your final percentage does not include a negative sign.
• Step Three : Divide that number by the actual value.
• Step Four: Multiply your result by 100.
• Step Five: Write out your final answer as a percentage.

Examples of How to Calculate Percent Error

We're now ready to take the percentage error formula out for a test drive.

Let's say you're a bookworm with a long vacation coming up. You go to the library to grab some reading material. Before you open the front door, you assume you'll check out three books. But instead, for whatever reason, you only take home two books. What's the percentage error of your estimate?

In our example, the experimental value is 3 and the actual value is 2. Plug in the numbers, and you get this:

Percent Error = (3 – 2)/2 x 100

If you're old enough to read this article, we're guessing you already knew that 3 minus 2 equals 1. Which leaves us with:

Percent Error = 1/2 x 100

Divide 1 by 2 and you get the following:

Percent Error = 0.5 x 100

And 100 times 0.5 equals 50. But remember, we have to express our final answer as a percentage. When we do that, we learn the original guess you made had a percent error of 50%.

This example was all about quantity (i.e., the number of library books). But the percent error formula can also be applied to lots of other values — like speed, distance, mass and time.

Bearing that in mind, let's go through the formula again.

Suppose a college athlete thinks he'll need 45 seconds to finish a hardcore workout challenge. But when he hits the gym, the routine takes him 60 seconds to complete. What was the percent error of the time estimate he started out with (45 seconds)?

Percent error = (45 – 60)/60 x 100

Right off the bat, we've hit a complication. If you subtract 60 from 45, you get a negative number (-15 to be exact).

Divide -15 by 60 and you'll get -0.25, which is another negative value. And we can't stop there; we still need to multiply the -0.25 by 100, giving us an answer of -25. Does that mean the percent error is -25%?

The percent error between an estimated value and the actual value cannot be expressed as a negative . It's always written out as a positive value, whether the starting estimate was way too big or way too small.

Here's where our old friends "absolute error" and "relative error" come into play. The value of -15 is only the relative error. You need to take the absolute value of that before proceeding with the calculation. Once you have the absolute error of 15, you can divide that by 60 and multiply by 100 for a percent error of 25%.

New York Yankees legend Lawrence Peter Berra — better known by his nickname "Yogi" — has been credited as saying , "Baseball is 90 percent mental. The other half is physical." Math teachers are still chuckling about that one.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

Imaging the Universe

Percent error formula.

When you calculate results that are aiming for known values, the percent error formula is useful tool for determining the precision of your calculations. The formula is given by:

The experimental value is your calculated value, and the actual value is the known value (sometimes called the accepted or theoretical value). A percentage very close to zero means you are very close to your targeted value, which is good. It is always necessary to understand the cause of the error, such as whether it is due to the imprecision of your equipment, your own estimations, or a mistake in your experiment.

Example Question

The 17th century Danish astronomer, Ole Rømer, observed that the length of the eclipses of Jupiter by its satellites would appear to fluctuate depending on the direction Earth was traveling relative to Jupiter at the time of the eclipse. If Earth was traveling toward Jupiter, the eclipes of Jupiter by, say, Io, would last for a shorter amount of time, while if Earth was traveling away from Jupiter, the eclipses would appear to be longer. In 1676, he determined that this phenomenon was due to the fact that the speed of light was finite, and subsequently estimated its velocity to be approximately 220,000 km/s. The current accepted value of the speed of light is almost 299,800 km/s. What was the percent error of Rømer's estimate?

Experimental value = 220,000 km/s = 2.2 x 10 8 m/s

Actual value = 299,800 km/s = 2.998 x 10 8 m/s

So Rømer was quite a bit off by our standards today, but considering he came up with this estimate at a time when a majority of respected astronomers, like Cassini, still believed that the speed of light was infinite, his conclusion was an outstanding contribution to the field of Astronomy.

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How do I calculate the experimental and theoretical rotational inertia of a point mass?

I'm getting some weird results from a calculation I'm doing and quite honestly, I'm pretty sure it's due to human error. I do have an apparatus involved for the experimental process for my lab but I don't think it's what's causing the problem. I've come to the conclusion that my notes do not contain the right equations for these calculations.

For the theoretical masses, I know the total mass of the point masses and the distance from the axis to the masses. I'm pretty sure the equation of this is either 1/2mr^2 or just mr^2. The 1/2Mr^2 is from my notes but I think the correct answer would be mr^2. However the hanging mass lies on an apparatus that is a cylinder so 1/2Mr^2 could be correct.

The experimental part of the lab involved an apparatus that looked like a wheel which lowered a hanging mass on a string by turning the wheel (also by gravity). For the point mass and apparatus combined, I know the hanging mass, slope, and radius. I also know this data for the apparatus. I started out by finding the Force (which I was told is also equal to the torque) using the equation F=m(g-a). I know a is acceleration, but I'm not exactly sure how that factors out. From there I'd probably use τ = I α but I know the angular acceleration nor how to calculate it.

The next part of my lab involves calculating the experimental rotational inertia of the ring and disk, and I know the hanging mass, slop and radius of each one. Would that be where 1/2Mr^2 comes in?

• homework-and-exercises
• rotational-dynamics
• moment-of-inertia

• $\begingroup$ Do you mean something like this , because you mention a slope? Since your description of the experimental setup it not 100% clear to me. $\endgroup$ –  fibonatic Commented Jan 7, 2014 at 17:28
• $\begingroup$ Sort of, except exactly downward. $\endgroup$ –  Genevieve Commented Jan 7, 2014 at 18:50
• $\begingroup$ But what do you mean with the slope, or do you mean that you know that the slope it vertical? $\endgroup$ –  fibonatic Commented Jan 7, 2014 at 18:55
• $\begingroup$ To be honest, I'm not completely sure. We used some sort of a program to measure it. $\endgroup$ –  Genevieve Commented Jan 7, 2014 at 20:00
• $\begingroup$ It was similar to the device mentioned in this pdf: physics.gmu.edu/phys161/spring2009/… $\endgroup$ –  Genevieve Commented Jan 7, 2014 at 20:08

Moment of inertia The definition of (mass) moment of inertia of a point mass is $$ I=r^2m $$ However in the real world you don't encounter point masses, but objects with non-zero volume (finite density). And leads to an integral to determine moment of inertia $$ I=\int_m{r^2dm}=\int_V{\rho(r)r^2dV}=\int_x{\int_y{\int_z{\rho(x,y,z)(x^2+y^2+z^2)dz}dy}dx} $$ The solutions of this integral of a few bodies, with constant non-zero density within geometric volume and zero density outside of it, can be found here . For example the moment of inertia of thin rod rotating around its center of mass is equal to $I=\frac{mL^2}{12}$ and for a solid cylinder $I=\frac{mL^2}{2}$. Experimental setup In your experimental a string is on one end connected to the hanging mass, lead over the pulley and then wounded around a drum (the other end is also connected to the drum). This drum is of the object from which you would like to determine its moment of inertia and it is assumed that it can rotate freely (without slip) around its axis. According to your documentation you measure how far the pulley has rotated, I will call this angle $\theta$, and its first and second time derivative $\omega=\dot{\theta}$ and $\alpha=\ddot{\theta}$. The displacement of the hanging mass is related to the angular displacement of the pulley and its radius, $r_p$, assuming that the string does not slip, so $$ s=r_p\theta $$ where $s$ is the vertical downward displacement of the hanging mass. This displacement is equal to the amount of string unrolled from the drum (assuming that the string is not elastic), which means that the angular displacement of the object from which you would like to determine the moment of inertia, I will call this $\theta_I$, can be calculated from this the other way around using the radius of the drum $r_d$ $$ s=r_p\theta=r_d\theta_I\rightarrow\theta_I=\frac{s}{r_d}=\frac{r_p}{r_d}\theta $$ This linear correlation also applies to the $\omega$ and $\alpha$. The only force applied on this system (which can perform work) is gravity on the hanging mass. Using all this you can derive the equation of motion (possibly using free body diagrams and tension in the string).

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What is the accepted value in an experiment?

The accepted value of a measurement is the true or correct value based on general agreement with a reliable reference. For aluminum, the accepted density is 2.70g/cm3. The experimental value of a measurement is the value that is measured during the experiment.

Table of Contents

What is the difference between an accepted value and an experimental value called?

Percent error is used when comparing an experimental result E with a theoretical value T that is accepted as the “correct” value.

How close a value is to an accepted value?

Accuracy is a measure of how close a measurement is to the correct or accepted value of the quantity being measured. Precision is a measure of how close a series of measurements are to one another. Precise measurements are highly reproducible, even if the measurements are not near the correct value.

How do you find the accepted value for density?

The Density Calculator uses the formula p=m/V, or density (p) is equal to mass (m) divided by volume (V). The calculator can use any two of the values to calculate the third. Density is defined as mass per unit volume.

What is the accepted value in percent error?

The percent error is the absolute value of the error divided by the accepted value and multiplied by 100%. % Error = |experimental value−accepted value| accepted value. ×100%

What is the accepted value of copper?

The accepted value of copper is 8.96 g/mL.

Is the accepted value the actual value?

Accepted value is the level of agreement between the absolute measurement and the actual measurement. It represents how the results closely agree with one another.

What is experimental value and theoretical value?

The experimental value is your calculated value, and the theoretical value is your known value. A percentage very close to zero means you are very close to your targeted value, which is good.

What is true value physics?

The actual population value that would be obtained with perfect measuring instruments and without committing any error of any type, both in collecting the primary data and in carrying out mathematical operations.

What is the scientific definition of precision?

The closeness of two or more measurements to each other is known as the precision of a substance. If you weigh a given substance five times and get 3.2 kg each time, then your measurement is very precise but not necessarily accurate. Precision is independent of accuracy.

What is measured value?

A measured value is the value of a measurand provided by a measuring instrument or measuring device. It is used in metrology applications and is expressed as the product of numerical value and unit; it is also frequently standardised and given in percent.

What is accuracy and precision in measurement?

Accuracy reflects how close a measurement is to a known or accepted value, while precision reflects how reproducible measurements are, even if they are far from the accepted value. Measurements that are both precise and accurate are repeatable and very close to true values .

What is the accepted value of water?

Since water is the “standard” by which other liquids are measured, the mark for water is probably labeled as “1.000”; hence, the specific gravity of water at about 4°C is 1.000.

What is the accepted value of lead?

The accepted values for the densities of aluminum, lead and copper are 2.70, 11.34 and 8.94 g/ml, respectively. You determined the density of a cylinder composed of one of these metals.

What is the theoretical value?

Sometimes referred to as a fair or hypothetical value, a theoretical value is the estimated price of an option. Sometimes referred to as a fair or hypothetical value, a theoretical value is the estimated price of an option. The options pricing may have to do with buying, selling, or a combination of the two.

What is the accepted value of aluminum?

The accepted value for the density of aluminum is 2.699 g/cm3.

What is percent error physics?

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

What is observed value?

observed value means a numerical value that represents observed or imputed information to the best of knowledge based on all available 2021 census information, in particular before the application of any statistical disclosure control measures; Sample 1Sample 2.

What is the accepted value of zinc?

The presently accepted value for the atomic weight of zinc is 65.37 [1 , 2].

What is the accepted value for the specific heat of copper?

The accepted value of the specific heat of copper is 0.385 J/g∙°C.

What is the meaning of actual value?

Definition. Actual value is the customer’s current and future value if the current level of business is maintained over time. This dimension of value includes revenue, but also elements such as how engaged the customer is in the business, communications, and referrals.[1]

What percent difference is acceptable?

Explanation: In some cases, the measurement may be so difficult that a 10 % error or even higher may be acceptable. In other cases, a 1 % error may be too high. Most high school and introductory university instructors will accept a 5 % error.

How do you find the experimental value in physics?

Complex Experiments Require an Average During these types of experiments, taking the average of the recorded results is understood to be the experimental value. The formula for the experimental value of a set of five numbers adds all five together and then divides the total by the number 5.

Why are theoretical and experimental values different?

This difference is due to three factors: the variation of the diffusion voltage, the nonzero electric field at the boundaries of the depletion region, and the contribution of electrons and holes. The exact values also disagree with the experimental results.

What is the difference between theoretical and experimental?

The difference between theoretical and experimental probability is that theoretical is based on knowledge and mathematics. Experimental probability is based on trials or experiments. Theoretical probability is what should happen. Experimental probability is what does happen.

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Finding gravity through experimental data

• Thread starter BayernBlues
• Start date Oct 13, 2007
• Tags Data Experimental Experimental data Gravity
• Oct 13, 2007

Homework Statement

Homework equations, the attempt at a solution.

• Findings from experimental setup demonstrate potential for compact and portable nuclear clocks
• Generating spin currents directly using ultrashort laser pulses
• A fundamental magnetic property of the muon measured to unprecedented precision

A PF Organism

It gives you the values of x and t, you have the equation that relates them. Solve for g.  

• Oct 20, 2007

FAQ: Finding gravity through experimental data

In an experiment, gravity can be measured by using a device called a gravimeter, which measures the acceleration due to gravity (g). This device uses a mass and spring system to measure the effects of gravity on an object.

The relationship between mass and gravity is described by Newton's Law of Universal Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The acceleration due to gravity can be calculated by using the equation g = F/m, where g is the acceleration due to gravity, F is the force of gravity, and m is the mass of the object experiencing the force of gravity. This can be done by plotting the data points and finding the slope of the best-fit line.

Some common sources of error in gravity experiments include air resistance, friction, and human error in taking measurements. Other factors such as the curvature of the Earth and variations in local gravitational fields can also affect the results.

Gravity affects the motion of objects by exerting a force on them that causes them to accelerate towards the center of the Earth. This acceleration is constant and can cause objects to fall towards the ground or orbit around larger objects, such as the Moon orbiting the Earth.

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How you can Calculate Experimental Value

Percent Error Formula . When you calculate results that are aiming for known values, the percent error formula is useful tool for determining the precision of your calculations. The formula is given by:

So Rømer was quite a bit off by our standards today, but considering he came up with this estimate at a time when a majority of respected astronomers, like Cassini, still believed that the speed of light was infinite, his conclusion was an outstanding contribution to the field of astronomy.

Video advice: How to calculate PERCENT ERROR of an experiment!

This video shows how to calculate percent error of an experiment, using the given Theoretical value and using obtained experimental value.

The experimental value is your calculated value, and the theoretical value is your known value. A percentage very close to zero means you are very close to your targeted value, which is good. It is always necessary to understand the cause of the error, such as whether it is due to the imprecision of your equipment, your own estimations, or a mistake in your experiment. Example: The 17th century Danish astronomer, Ole Rømer, observed that the periods of the satellites of Jupiter would appear to fluctuate depending on the distance of Jupiter from Earth. The further away Jupiter was, the longer the satellites would take to appear from behind the planet. In 1676, he determined that this phenomenon was due to the fact that the speed of light was finite, and subsequently estimated its velocity to be approximately 220,000 km/s. The current accepted value of the speed of light is almost 299,800 km/s. What was the percent error of Rømer’s estimate? Solution:experimental value = 220,000 km/s = 2.

Video advice: How to calculate experimental error

I go over how to calculate experimental error.

Video advice: Experimental Error Calculations – Part 1

This this is 2 part series on how to calculate experimental error. The theoretical values that are available in textbooks, published charts, and reference books are discussed along with what it means to have an experimental value

How do you find theoretical and experimental value?

Alternate Wording. Accepted value is sometimes called the “true” value or “theoretical” value, so you might see the formula written in slightly different ways: PE = (|true value – experimental value| true value) x 100%.

What is experimental value and theoretical value?

The experimental value is your calculated value, and the theoretical value is your known value . A percentage very close to zero means you are very close to your targeted value, which is good.

How do you find the experimental value in percent error?

Steps to Calculate the Percent Error Subtract the accepted value from the experimental value . Divide that answer by the accepted value. Multiply that answer by 100 and add the % symbol to express the answer as a percentage.

How do you calculate experimental volume?

0:293:55Calculating Molar Volumes Using Experimental DataYouTubeStart of suggested clipEnd of suggested clipFrom this type of experiment pause calculate and continue when ready. The answer is to divide 0.625MoreFrom this type of experiment pause calculate and continue when ready. The answer is to divide 0.625 liters of oxygen produced by 0.83 grams this means that 1 gram of oxygen.

What is experimental value in physics?

The experimental value is the value that you get in an experiment . The absolute value of the difference between the two values (the "error") is your experimental error. ... For example, suppose that you did an experiment to determine the boiling point of water and got a value of 99.3 °C. Your experimental value is 99.3 °C.

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• How you can Calculate RPD

Erwin van den Burg

Stress and anxiety researcher at CHUV2014–present Ph.D. from Radboud University NijmegenGraduated 2002 Lives in Lausanne, Switzerland2013–present

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