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Percent Error Calculator
Percent error is |measured − accepted| ÷ |accepted| × 100. A measured density of 2.85 against an accepted 2.70 is an error of 0.15, and 0.15 ÷ 2.70 × 100 = 5.56%. Divide by the accepted value, not your own result. This calculator also handles several trials at once.
Measured against accepted, in percent.
- The error: measured minus accepted = 2.85 − 2.7 = 0.15.
- Divide its size by the size of the accepted value: 0.15 ÷ 2.7 = 0.0(5).
- Multiply by 100: 5.(5)%, 5.56% to 2 decimal places.
- The measurement is above the accepted value.
| Result | Value |
|---|---|
| Percent error | 5.56% |
| Signed percent error | +5.56% |
| Absolute error | 0.15 |
| Relative error (as a decimal) | 0.0556 |
| Percent difference, if neither value were the true one | 5.41% |
The figures above are an example (a measured density of aluminium against 2.70 g/cm³): put in your own. For several trials, type the measurements separated by spaces, semicolons or a comma and a space, such as 9.6, 9.9, 10.2; the mean is compared with the accepted value and each trial gets its own row. Worked out exactly in this browser and kept there; nothing is sent anywhere.
Enter your measurement, or several separated by spaces, and the accepted value. You get the percent error, signed or absolute, the error of the mean and of each trial, and the working in order.
Percent error is how far a measured value is from an accepted (true or reference) value, as a percentage of the accepted value. It measures accuracy: how close a result is to the value it should have.
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- Nothing uploaded
- Shows every step
- Works offline
- Exact, no rounding errors
Key facts
| Detail | Answer |
|---|---|
| Formula | |measured − accepted| ÷ |accepted| × 100 |
| Example | 2.85 against 2.70: 5.56% |
| Trials | Up to 50 measurements, compared through their mean |
| Signed option | + when over the accepted value, − when under |
| Refuses | An accepted value of 0, where percent error is undefined |
| Where your numbers are kept | This browser only |
How to calculate percent error
Subtract, take the size, divide by the accepted value, multiply by 100.
Enter the measured value
Your result; for several trials, separate them with spaces.
Enter the accepted value
The true, theoretical or reference value you are checking against.
Subtract
Measured minus accepted gives the error, with its sign.
Divide by the accepted value
Use its size, ignoring any minus sign.
Multiply by 100
That is the percent error.
Choose signed or absolute
Signed keeps whether you were over or under.
Who uses a percent error calculator
Anyone comparing a result with the value it should have been.
Chemistry students
A titration or density result against the textbook value.
Physics students
g from a pendulum, the speed of sound, a resistor’s value.
Teachers
Marking a set of lab reports against one accepted value.
Technicians
A reading checked against a calibration standard.
Bakers and makers
A kitchen scale checked against a known weight.
Forecasters
A forecast compared with what actually happened.
Divide by the accepted value: percent error and its look-alikes
Percent error divides by the accepted value, the figure you are checking against, never by your own measurement. That is the single most common slip in lab reports, and it changes the answer: for a measured 2.85 against an accepted 2.70, dividing by 2.70 gives 5.56%, while dividing by 2.85 gives 5.26%. Only the first is the percent error.
| Measure | Formula | For 2.85 against 2.70 | Use it when |
|---|---|---|---|
| Percent error | |measured − accepted| ÷ |accepted| × 100 | 5.56% | One value is the reference: a textbook constant, a certified standard |
| Signed percent error | (measured − accepted) ÷ |accepted| × 100 | +5.56% | You need to know whether you were over or under |
| Percent difference | |a − b| ÷ ((a + b) ÷ 2) × 100 | 5.41% | Two measurements, neither of them the true value |
| Relative error | |measured − accepted| ÷ |accepted| | 0.0556 | The same ratio, not multiplied by 100 |
The underlying idea comes from metrology. The International Vocabulary of Metrology, JCGM 200:2012, entry 2.16, defines measurement error as the “measured quantity value minus a reference quantity value”. Percent error is that error as a percentage of the reference. The VIM also notes the error can only be known when a reference value really exists, such as a calibrated standard; for an unknown true value, what you can state is an uncertainty, not an error.
Percent error over several trials
Lab work rarely stops at one measurement. When you have several trials, there are two sensible numbers to report, and the calculator gives both: the percent error of the mean (how accurate the method is overall) and each trial’s own signed error (how much they scatter). Type the trials separated by spaces.
| Measurement | g in m/s² | Error against 9.81 |
|---|---|---|
| Trial 1 | 9.6 | −2.14% |
| Trial 2 | 9.9 | +0.92% |
| Trial 3 | 10.2 | +3.98% |
| Mean | 9.9 | +0.92% |
The mean of 9.6, 9.9 and 10.2 is 9.9, which is 0.92% above 9.81, although two of the three trials were further out than that. A small error of the mean with a wide spread says the method is accurate but not precise; a large error with a tight spread says the opposite: something systematic, such as a miscalibrated scale, pushes every reading the same way. The calculator lists the spread (highest minus lowest) beside the trials. Standard gravity, for reference, is defined as exactly 9.80665 m/s², so 9.81 is itself a rounded accepted value: say which you used.
Is my percent error good?
What counts as a good percent error depends on the experiment, not on a universal cut-off. A school pendulum, a burette titration and a kitchen scale each have their own limits. As a rough guide used in many teaching labs, the table below gives typical ranges; your course or method sets the real one.
| Percent error | What it usually means |
|---|---|
| Under 1% | Careful work with good instruments; typical of a titration done well |
| 1% to 5% | Usual for school and first-year experiments with simple equipment |
| 5% to 10% | Worth explaining: reaction time, heat loss, reading a scale |
| Over 10% | Look for a mistake: units, a wrong accepted value, a misread scale, a slip in the formula |
Percent error can exceed 100%: measuring 25 when the accepted value is 10 is a 150% error. It is undefined when the accepted value is 0, since that would mean dividing by 0; the calculator refuses and asks for the absolute error instead. Rounding the answer to more places than the measurements justify adds nothing: measurements to three significant figures support a percent error to about two. Percent error is one of the Grade 7 percent problems in the Common Core (7.RP.A.3), alongside percent increase and decrease, which is why it is often first met outside a lab.
What this calculator does not do
This calculator compares measurements with one accepted value. It does not work out measurement uncertainty, standard deviation, confidence intervals or significant figures for you, and it cannot tell you which accepted value is right for your conditions: a density, the speed of sound or g all vary with temperature, altitude or purity, so take the accepted value from your course or a data book. Up to 50 measurements can be entered; decimals with a comma (2,85) and thousands separators (1,500) are read too, so separate measurements with spaces, semicolons or a comma followed by a space (9.6, 9.9), not a bare comma.
For a change between two values with no true value, use the percentage change calculator’s percent difference; for the average of a long list of readings with its median and range, the average calculator. Counting colonies or cells before working out an error? The colony count guide explains how counting error itself limits the result.
This calculator or an answer-only one
What this page does that a typical answer-only widget does not.
| This page | A typical calculator | |
|---|---|---|
| Several trials | Mean and each trial | One value only |
| Signed error | Over or under, your choice | Absolute only |
| Related measures | Relative error, percent difference | Not shown |
| Shows the working | Every step | Answer only |
| Exact arithmetic | No floating-point drift | Floating point |
| Your numbers leave the browser | Never | Varies |
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Frequently asked questions
What is the formula for percent error?
Percent error = |measured value − accepted value| ÷ |accepted value| × 100. The vertical bars mean take the size and ignore the sign. For a measured 2.85 and an accepted 2.70: 0.15 ÷ 2.70 × 100 = 5.56%. The accepted value is also called the true, theoretical or reference value.
Do you divide by the experimental or the accepted value?
The accepted value. Percent error measures how far you are from the value you should have got, so that value is the base. Dividing by your own measurement gives a different number (5.26% instead of 5.56% in the example) and is a common mistake in lab reports.
Can percent error be negative?
The standard formula uses absolute values, so it is never negative. Some courses use a signed percent error instead, positive when the measurement is too high and negative when it is too low. The calculator offers both; the signed version keeps the direction, which helps spot a systematic error.
Can percent error be more than 100%?
Yes. If the measurement is more than double the accepted value, the error is over 100%: 25 against an accepted 10 is 150%. A result below the accepted value can only reach 100%, when the measurement is 0. An error that large usually points to a unit or formula mistake.
What is a good percent error?
It depends on the experiment and the equipment, not on a fixed rule. Many teaching labs treat under 5% as good for simple apparatus and under 1% as careful work. Larger errors are worth explaining: heat loss, reaction time, a scale read at an angle, impure samples.
How do I find percent error with several trials?
Average the trials first and compare the mean with the accepted value; then give each trial’s own error to show the scatter. Type the trials separated by spaces in the calculator: 9.6 9.9 10.2 against 9.81 gives a mean of 9.9 and a percent error of 0.92%.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known true value and divides by that value. Percent difference compares two measurements when neither is the true one, dividing by their average. For 2.85 and 2.70 they are 5.56% and 5.41%. Use percent error only when one value is known to be right.
What if the accepted value is zero?
Percent error is not defined, because it would mean dividing by zero. Report the absolute error instead, the measured value minus the accepted one, in the measurement’s units. The calculator refuses an accepted value of 0 with a message saying so.
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