How this percent error calculator works
Percent error tells you how close a measurement is to a known, accepted value. It is one of the most common ways to report accuracy in science and engineering labs because it scales the size of the mistake to the size of the thing being measured.
The calculator takes your experimental value (what you measured or observed) and your theoretical value (the accepted or exact value), then computes the difference, takes its absolute value, divides by the absolute value of the theoretical value, and multiplies by 100. It also reports the plain absolute error (the raw size of the difference) and the signed relative error, whose sign shows whether you over- or under-estimated.
Reference note: the theoretical (accepted) value cannot be zero, because dividing by zero is undefined. If it is zero, use absolute error instead, or compare against a non-zero reference.
Frequently asked questions
- What is percent error?
- Percent error measures how far a measured (experimental) value is from a known accepted (theoretical) value, expressed as a percentage of the accepted value. A smaller percent error means the measurement is closer to the true value.
- How do I calculate percent error?
- Subtract the accepted value from the measured value, take the absolute value of that difference, divide by the absolute value of the accepted value, then multiply by 100: percent error = |observed − true| / |true| × 100.
- Can percent error be negative?
- The standard percent error uses absolute value, so it is never negative. A signed version drops the absolute value and keeps the sign: positive means an over-estimate (too high) and negative means an under-estimate (too low).
- What is a good percent error?
- It depends on the context. In many school labs a percent error under about 5% is considered good, while precise physics or chemistry work may require well under 1%. The acceptable threshold is set by the experiment and equipment.
- What is the difference between percent error and percent difference?
- Percent error compares a measurement to a known accepted value, dividing by that accepted value. Percent difference compares two experimental values when neither is the standard, dividing by their average. Use percent error only when you have a true reference value.
- Why use absolute value in percent error?
- The absolute value reports the size of the error regardless of direction, so an over- and under-estimate of the same magnitude give the same percent error. If you also care whether the measurement was high or low, use the signed percent error.