Percent Error Calculator

What this calculator does

You ran the experiment, you got a number, and there is a known value it was supposed to land near. How close did you get? Percent error is the standard lab answer, in physics and chemistry, comparing what you measured against the accepted figure.

The accepted (theoretical) value is what it should be; the experimental value is what you actually got. Type both, and the tool gives you the percent error.

Using the calculator

1. Type the theoretical value, the accepted or expected result.
2. Type the experimental value, the one you measured.
3. Press Calculate.

Neither value can be zero. The result is always positive, since it measures the size of the error rather than its direction.

The formula | |theoretical − experimental| ÷ |theoretical| × 100

Percent error is:

(|theoretical − experimental| ÷ |theoretical|) × 100

Take the gap between the two values, ignoring which is bigger, divide it by the theoretical value, and turn it into a percentage. The vertical bars are absolute value, so the error always comes out positive, no matter whether your measurement landed above or below the accepted figure.

Why it divides by the accepted value

The denominator is always the theoretical value, the one known to be correct, never your measurement. That is the point of the calculation: it asks how big your error is compared with what the answer should have been. Dividing by the accepted value also makes errors comparable across experiments of very different sizes, since each is scaled against its own expected result.

Error, change, or difference?

Percent error is one of three close cousins that all compare two numbers as a percentage, and they differ only in what they divide by. That one choice is the whole story.

• Percent error divides by the accepted true value, for when one number is known to be correct. That is this tool.
• Percent change divides by the starting value, for a before-and-after over time. See the percent change calculator.
• Percent difference divides by the average, for two measurements of equal standing where neither is the reference. See the percent difference calculator.

A worked example | theoretical 70, experimental 100

Say the accepted value is 70 and you measured 100.

1. The gap: |70 − 100| = 30.
2. Divide by the theoretical value: 30 ÷ 70 = 0.4286.
3. As a percentage: 0.4286 × 100 ≈ 42.857%.

So the percent error is about 42.86%. For a more typical lab case, measuring water's boiling point at 101.5°C against the true 100°C gives |100 − 101.5| ÷ 100 × 100 = 1.5% error.

What the result tells you

A small percent error means your measurement sat close to the accepted value, which is to say it was accurate. A large one means it was well off. What counts as acceptable depends on the field: a general chemistry lab might be happy under 5%, while a physics experiment often wants under 1 or 2%. And a big error is not automatically a failed experiment, it can point to a systematic problem you can track down and correct.

Questions people ask

What is the percent error for a theoretical 70 and experimental 100?

About 42.86%. The gap of 30, divided by the theoretical 70, times 100.

What is the percent error formula?

(|theoretical − experimental| ÷ |theoretical|) × 100. The gap divided by the accepted value, as a percentage.

Which value goes in the denominator?

The theoretical, or accepted, value, never your measurement. Percent error is always measured against the known correct value.

How is this different from percent change or percent difference?

Only in the denominator. Error divides by the accepted true value, change divides by the starting value, and difference divides by the average of the two.

Can percent error be negative?

Not in this standard form. The absolute value makes it always positive, so it reports the size of the error, not its direction.

References

A note on the idea behind it. Percent error is the absolute gap between a measured and an accepted value, divided by the accepted value, as a percentage. It shares its structure with percent change and percent difference, differing only in the denominator: the accepted true value here, the starting value for change, and the average for difference. For further reading, see Approximation error.

1. Percent error, the absolute difference between a measured and an accepted value divided by the accepted value, expressed as a percentage.
2. The shared structure of percent error, percent change, and percent difference, distinguished by dividing by the true value, the starting value, or the average.