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How to calculate percent error — step by step

Q: Why do you take the absolute value?

Percent error describes the size of the deviation, not its direction. The absolute value in the numerator keeps the error positive whether the measurement was too high or too low.

Q: Is the error relative to the measured or the true value?

Always the true (theoretical) value. It sits in the denominator and acts as the yardstick. Dividing by the measured value instead would give a different, incorrect reference.

Q: What does a small percent error mean?

A small percent error means high accuracy: the measured value is close to the true value. 0.10% means the measurement is off by only a tenth of a percent.

Q: Where is percent error used?

In physics, chemistry and engineering to assess the accuracy of measurements, experiments and approximations — for example when comparing a measured value against a known reference value.

Q: How is it different from absolute error?

Absolute error is simply the deviation in the unit of the quantity, e.g. 0.01. Percent error expresses that deviation relative to the true value, making different measurements comparable.

Percent error measures how far a measured value lands from the accepted (true) value — relative to the true value. You take the absolute deviation, divide by the true value, and multiply by 100. Worked example: measured 9.8, true 9.81 → ≈ 0.10%. Suitable for percentages from Grade 7 / Year 8 onward.

By Valerij Hofmann · Fullstack Developer

Updated May 29, 2026Beginner

Quick answer

Percent error tells you how far a measured value lands from the true value — relative to the true value. The formula is |measured − true| ÷ |true| · 100. Example: 9.8 instead of 9.81 → |9.8 − 9.81| ÷ 9.81 · 100 ≈ 0.10%.

At a glance

Summary of this tutorial
Formula	\|measured − true\| ÷ \|true\| · 100
Method	Relative deviation as a percentage
Steps	4
Answer (9.8 vs 9.81)	≈ 0.10%
Reference value	True value (denominator)
Grade level	Grade 7 (ages 12–13)

Worked example: 9.8 vs 9.81

EXAMPLE

|9.8 − 9.81| ÷ 9.81 · 100

We compare the measured value 9.8 against the true value 9.81 and express the deviation as a percentage.

How to calculate percent error — the steps

These four steps work for any comparison of a measured value against a true value.

Step 1 · Start
|9.8 − 9.81| ÷ |9.81| · 100
Plug in the measured value 9.8 and the true value 9.81.
Step 2 · Absolute
0.01 ÷ 9.81 · 100
Take the absolute deviation in the numerator — it is always positive.
Step 3 · ÷ true
0.00102 · 100
Dividing by the true value gives the relative ratio.
Step 4 · · 100
≈ 0.10%
Multiplying by 100 turns the ratio into the percent error.

Why the formula works

A raw deviation like 0.01 tells you nothing about accuracy until you know how big the values are. Dividing by the true value makes the deviation relative — 0.01 against a value of 9.81 is tiny, but the same 0.01 against a value of 0.1 would be huge. Multiplying by 100 turns that ratio into a percentage, and the absolute value in the numerator keeps the error positive whether you measured too high or too low.

Practice it yourself

Open the percent error calculator

Enter your own values. See every step.

Start practice set

Percent error problems

Frequently asked questions

How do you calculate percent error?

Take the absolute deviation between the measured and true value, divide by the absolute true value, and multiply by 100: |measured − true| ÷ |true| · 100. Example: 9.8 instead of 9.81 → |9.8 − 9.81| ÷ 9.81 · 100 ≈ 0.10%.

Why do you take the absolute value?

Is the error relative to the measured or the true value?

What does a small percent error mean?

Where is percent error used?

How is it different from absolute error?

Quick answer

At a glance

Worked example: 9.8 vs 9.81

How to calculate percent error — the steps

Step 1 · Start

Step 2 · Absolute

Step 3 · ÷ true

Step 4 · · 100

Why the formula works

Practice it yourself

Frequently asked questions