The formula this page uses
percent error = |measured − accepted| ÷ |accepted| × 100%
Percent Error Calculator
Use the free percent error calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Arithmetic
Percent Error Calculator explained
The short version
- Percent error says how far your measurement landed from the value the book says is correct.
- The answer is never negative, because the bars in the formula turn the gap into a plain distance.
- Divide by the accepted value, not by your own measurement, or two labs cannot be compared.
What each part means
SymbolWhat it means
measured — Your valueWhat your experiment actually gave, in whatever unit you recorded, such as m/s² or grams.
accepted — The true valueThe published or theoretical value, in the same unit. It goes on the bottom of the division.
| | — Absolute value barsThey throw away the minus sign, so a gap of −0.19 counts as 0.19.
× 100 — The percent stepTurns the decimal fraction into a percent. Without it you get 0.019 instead of 1.94%.
Show your work: a full example
- A pendulum experiment measures gravitymeasured = 9.62 m/s², accepted = 9.81 m/s²
- Subtract to get the gap9.62 − 9.81 = −0.19
- Drop the minus sign|−0.19| = 0.19
- Divide by the accepted value0.19 ÷ 9.81 = 0.019368
- Multiply by 1000.019368 × 100 = 1.9368
- Round to two decimal places1.94%
- Say what it meansthe measurement came out about 2 percent below the true value
A second, different case
- A different case: there is no accepted valuetwo students measure the same liquid as 27.5 mL and 25.0 mL
- Take the gap between them|27.5 − 25.0| = 2.5
- Use their average as the bottom(27.5 + 25.0) ÷ 2 = 26.25
- Divide2.5 ÷ 26.25 = 0.095238
- Multiply by 1000.095238 × 100 = 9.52%, which is the percent difference
- Compare with percent error if 25.0 were the true value2.5 ÷ 25.0 × 100 = 10.00%
- Read the gap between the two answersthe bottom number changed from 26.25 to 25.0, and that alone moved the answer by half a percent
Copy-ready example
measured = 9.62 m/s², accepted = 9.81 m/s²
A pendulum experiment measures gravity
Questions about the Percent Error Calculator
Can percent error be bigger than 100%?
Yes. If the accepted value is 5 and you measured 12, the gap is 7 and 7 ÷ 5 × 100 = 140%. It just means your measurement was more than twice what it should have been, which usually points at a unit mix-up rather than sloppy reading.
What is the difference between percent error and percent difference?
Percent error needs one value you trust, and that trusted value goes on the bottom. Percent difference is for two measurements where neither is the truth, so you put their average on the bottom instead. Same subtraction on top, different bottom.
How many decimal places should my percent error have?
Match the measurement. If you read 9.62 off a timer with three digits, quoting 1.9368% pretends you knew more than you did. Two digits after the point, or even one, is honest for most school labs.
What if the accepted value is zero?
Then percent error does not exist, because you cannot divide by zero. This happens with things like a net charge or a zeroed force reading. Report the plain gap, called the absolute error, and say what unit it is in.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.