Math & Statistics · Browser · Free

Percent Error Calculator

Put in the value you measured or approximated and the exact value it was meant to match, and this tool shows the error between them as a percentage of the exact value. It also gives the same error with its sign kept, plus the plain difference between the two numbers.

What this calculator does

Fill in the two number fields — the approximated (measured) value and the exact (actual) value — and press Calculate. Result cards then appear below the button, one for percent error, one for percent error non absolute, and one for absolute error.

Percent error states the gap as a share of the exact value rather than as a raw amount, so the same gap between two numbers reads larger when the exact value is smaller. With an approximated value of 12 and an exact value of 10 it reports 20 %, while an approximated value of 10 against an exact value of 12 reports about 16.6666666666667 %.

Percent error non absolute is the second reading of the same pair of inputs and can come out negative: for an approximated value of 10 and an exact value of 12 it shows about -16.6666666666667 % where the percent error shows about 16.6666666666667 %. The absolute error card leaves percentages aside and gives the size of the gap itself, which is 2 for that pair.

Copy writes a result together with its unit to the clipboard, and Clear resets the form so you can start again with a new pair of values.

Percent error formula

The absolute error is the difference between the exact value and the approximated value, taken as a size: ε = |V_exact - V_approx|.

The percent error is 100% multiplied by that absolute error and divided by the exact value: δ = 100% × |V_exact - V_approx| / |V_exact|. Dividing by the exact value is what turns the gap into a percentage of it.

Worked through, an approximated value of 12 with an exact value of 10 gives δ = 100% × |10 - 12| / |10| = 20%, and the absolute error is 2. An approximated value of 2.5 with an exact value of 2.0 gives δ = 100% × |2 - 2.5| / |2| = 25%, with an absolute error of 0.5.

The same route with an approximated value of 10 and an exact value of 12 gives δ = 100% × |12 - 10| / |12| ≈ 16.6666666666667%, and the percent error non absolute card shows ≈ -16.6666666666667% for that same pair.