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Math

Percent Error Calculator

Calculate percent error between an experimental value and a theoretical or accepted value. Used in science and engineering.

What is Percent Error Calculator?

Percent error measures how close an experimental or measured value is to a known theoretical or accepted value, expressed as a percentage. It is widely used in chemistry, physics, and engineering labs to evaluate the accuracy of measurements and experiments.

How to use

  1. 1 Enter your experimental (measured) value in the first field.
  2. 2 Enter the theoretical (accepted or true) value in the second field.
  3. 3 The percent error, absolute error, and relative error all appear instantly.
  4. 4 A positive result means you overestimated; a negative result means you underestimated.

Formula

Percent error = (|Experimental - Theoretical| / |Theoretical|) × 100. Absolute error = Experimental - Theoretical. Relative error = (Experimental - Theoretical) / Theoretical.

Example calculation

If you measured gravity as 9.8 m/s² and the accepted value is 9.81 m/s², the percent error is |9.8 - 9.81| / 9.81 × 100 ≈ 0.102%. The absolute error is -0.01 m/s² (an underestimate).

Frequently asked questions

What is the difference between percent error and percentage change?

Percent error compares a measured value to a known accepted value to assess accuracy. Percentage change compares two values over time without implying one is 'correct'.

Why do we use the absolute value in the percent error formula?

Taking the absolute value gives a non-negative percent error representing the magnitude of inaccuracy. The sign of the absolute error separately tells you if you over- or underestimated.

What is a good percent error?

It depends on the field. In many physics experiments, under 5% is acceptable. In chemistry or engineering, tighter tolerances (under 1–2%) may be required.

What is the difference between absolute error and relative error?

Absolute error is the actual numerical difference (Experimental - Theoretical). Relative error is that difference divided by the theoretical value, giving a unitless ratio.

What does a percent error of 0% mean?

A 0% percent error means your measured value exactly matches the accepted value — a perfect measurement, which is rare in practice.