Percentage Error Calculator

What this calculator does

You made a call, and reality came in different. A forecast, a rough estimate, a guess at a total. How far off were you, as a percentage? That is percentage error, the everyday cousin of the lab's percent error, comparing your estimate against what actually happened.

Your estimate is the prediction; the actual value is the real result. Type both, and the tool gives you the percentage error.

Using the calculator

1. Type the estimated value, your prediction or guess.
2. Type the actual value, what really happened.
3. Press Calculate.

The result is always positive, since it measures how far off the estimate was, regardless of direction.

The formula | |estimated − actual| ÷ actual × 100

Percentage error is:

(|estimated − actual| ÷ actual) × 100

Take the gap between your estimate and the real value, ignoring which is bigger, divide it by the actual value, and turn it into a percentage. The absolute value keeps the result positive whether you guessed too high or too low.

Why it divides by the actual value

The denominator is the actual value, the real one, not your estimate. The whole question is how big your miss was relative to the truth, so the truth is what you measure against. A 10 unit miss means something quite different against an actual of 20 than against an actual of 2,000, and dividing by the actual value captures that.

A worked example | estimated 90, actual 100

Say you estimated 90 and the real figure turned out to be 100.

1. The gap: |90 − 100| = 10.
2. Divide by the actual value: 10 ÷ 100 = 0.1.
3. As a percentage: 0.1 × 100 = 10%.

So the estimate was off by 10%. If you had forecast 90 sales and made 100, your forecast was 10% under.

The same calculation, framed for estimates

This is the very same calculation as the percent error calculator, which labels its inputs experimental and theoretical for science labs. This one uses estimated and actual, which fits forecasts and everyday estimates more naturally. Both work out the gap divided by the true value. And like its lab twin, it belongs to a trio: percent change divides by the starting value, and percent difference divides by the average, while this one divides by the actual, true value. The denominator is what makes it an error.

Where it shows up

Anywhere you want to know how close a prediction came. Forecasting sales, demand or budgets and checking against the real numbers. Estimating a count or a measurement and comparing with the true figure. Judging how accurate a model or a rule of thumb turned out to be. It is the standard "how close was I?" check.

Questions people ask

What is the percentage error for an estimate of 90 and an actual of 100?

10%. The gap of 10, divided by the actual 100, times 100.

What is the formula?

(|estimated − actual| ÷ actual) × 100. The gap divided by the actual value, as a percentage.

Which value is the denominator?

The actual value, the real result, not your estimate. The error is always measured against the truth.

Is this the same as percent error?

Yes, the same calculation. This version uses estimated and actual for forecasts, while the percent error calculator uses experimental and theoretical for science.

How does it relate to percent change and percent difference?

They share one structure and differ in the denominator: actual value for error, starting value for change, average for difference.

References

A note on the idea behind it. Percentage error is the absolute gap between an estimated and an actual value, divided by the actual value, as a percentage. It is the same measure as percent error under different labels, and shares its structure with percent change and percent difference, set apart by dividing by the true value. For further reading, see Approximation error.

1. Percentage error, the absolute difference between an estimated and an actual value divided by the actual value, expressed as a percentage.