About the Percent Error Calculator
Percent Error Calculator has three modes for comparing two numbers. Percent error compares a measured value with the true or accepted value, the calculation used in science labs. Percent difference compares two values when neither is the true one, using their average as the base. Percent change shows how much a value went up or down from an old value to a new one, labelled as an increase or a decrease. Each mode shows the answer, the signed version so that you can see the direction, and the formula that was used. The tool refuses cases where the calculation is not defined, such as a true value of zero, and explains why. Values can be negative or decimal, and everything is calculated in your browser.
Updated September 2026
How to use the Percent Error Calculator
- 1Choose Percent error, Percent difference or Percent change.
- 2Type the two values. For percent error, first the measured value and then the true value.
- 3Read the percentage in the big result box.
- 4Check the signed value to see whether it is above or below, or an increase or decrease.
- 5Look at the formula in the smaller box if you want to show your working.
Percent error in science lessons
Percent error tells you how far a measurement is from the accepted value, as a percentage of that value. It is used in physics, chemistry and biology labs to judge accuracy: the density of a metal sample against a table value, the boiling point of a liquid, or the acceleration due to gravity from a pendulum.
A small percent error means your method was accurate. A large one suggests a systematic problem, such as a badly calibrated scale or heat loss, or simply an outlier reading. Repeating the measurement and averaging the results usually brings the error down.
Choosing the right mode
- Percent error: one number is the truth or a reference value.
- Percent difference: two numbers of equal standing, such as two lab groups' results or two shops' prices.
- Percent change: a value that moved from a starting point to a new one over time, such as sales or a bill.
- Order matters for percent error and percent change, but not for percent difference.
Working examples
A student finds the density of aluminium to be 2.55 g/cm³ where the accepted value is 2.70. The percent error is |2.55 − 2.70| ÷ 2.70 × 100 = 5.56 percent, and the signed value is −5.56 percent, so the result was too low. Two thermometers read 21.4 and 22.0 degrees, so their percent difference is 0.6 ÷ 21.7 × 100 = 2.76 percent. A monthly bill going from 120 to 138 is a 15 percent increase.
If a percentage seems too large, check whether you put the values in the right boxes. Swapping measured and true changes the base and gives a different answer.
Tips and related tools
Keep the same units for both values, and do not round before the calculation. For a more general percentage tool, Percentage Calculator handles finding a percent of a number and increasing or decreasing an amount. Standard Deviation Calculator shows how spread out repeated measurements are, and Average Calculator gives the mean of several readings that you can use as your measured value.
Ratio Calculator and Profit Margin Calculator help when you compare amounts in business, and Discount Calculator turns a percent decrease into a sale price.
Features
- Percent error against a true value
- Percent difference between two values
- Percent change with increase or decrease label
- Signed result shows the direction
- Formula shown for each mode
- Handles decimals and negative numbers
- Runs in your browser
Frequently asked questions
What is the percent error formula?
Percent error = |measured − true| ÷ |true| × 100. If you measured 9.6 metres per second squared for gravity and the accepted value is 9.81, the difference is 0.21, and 0.21 ÷ 9.81 × 100 is about 2.14 percent.
Can percent error be negative?
The usual definition takes the absolute value, so percent error is positive. Some teachers keep the sign to show whether the measurement was too high or too low, so the tool shows both the absolute and the signed version.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a value you know is right, so the true value is the base. Percent difference compares two values that are equally good, such as two measurements or two prices, so it uses their average as the base and does not depend on the order.
How do I calculate percent change?
Subtract the old value from the new one, divide by the old value and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25 percent increase. Going from 100 back to 80 is a 20 percent decrease, which shows that increases and decreases are not symmetrical.
Why can't the true value be zero?
Percent error divides by the true value, and division by zero is not defined. If the true value is zero, report the absolute error, which is the plain difference, instead of a percentage.
What is a good percent error?
It depends on the experiment. In a school lab, under 5 percent is often considered good and under 10 percent acceptable. Precise instruments and professional experiments aim for well under 1 percent. Your teacher or the method sets the standard.