Percent Error Calculator — How Close Is Your Measurement?
Enter a measured value and the actual (accepted) value to get percent error — plus absolute error, relative error, and the signed difference, so you can see direction, not just size.
Your values
🔒 All calculations happen in your browser — no data leaves your device.
Your error
How the two values compare
Bar lengths show the size of each value; the gap between them is your error.
- Percent error = |measured − actual| ÷ |actual| × 100: a measured 9.8 against an actual 10 is 2.00% — graded “Good — small error” on the page’s own scale.
- Alongside the headline you get absolute error (0.2), relative error (0.02) and the signed difference (−0.2), so direction is visible, not just size.
- An actual value of 0 makes percent error undefined — division by zero — so switch to absolute error; signed mode keeps the sign when the direction matters.
Enter a measured value and the actual (accepted) value to get percent error instantly — plus absolute error, relative error, and the signed difference, so you can see direction, not just size.
Keep exploring
Three companion tools for measurement and percent work.
How it works
Three steps from a reading to a verdict.
Enter your measured value
Type the number your experiment, instrument, or estimate produced.
Enter the actual value
Type the accepted, true, or theoretical value you are checking against.
Read the error
See percent error, the raw gap, and whether your measurement ran high or low.
The math behind percent error
Percent error measures how far a measurement is from the accepted value, scaled by that value — so a 0.2 miss matters a lot against 10, and barely at all against 10,000:
Worked examples:
| Values | Calculation | Result |
|---|---|---|
| Measured 9.8, actual 10 | |9.8 − 10| ÷ |10| × 100 | 2.00% |
| Measured 105, actual 100 | |105 − 100| ÷ |100| × 100 | 5.00% |
| Measured 49.5, actual 50 | |49.5 − 50| ÷ |50| × 100 | 1.00% |
| Measured 10, actual 10 | |10 − 10| ÷ |10| × 100 | 0.00% — perfect match |
Go deeper
The details that separate a rough guess from a trustworthy number.
- Percent error compares a measurement to a known accepted value — divide by the actual value. Use it when a true value exists (lab work, calibration, forecasts scored against outcomes).
- Percent difference compares two values with no accepted truth — divide by their average. Use it when comparing two methods, two instruments, or two measurements of the same thing.
- Example: 9.8 vs 10 gives 2.00% error (vs. actual 10), but a 2.02% percent difference (vs. the average 9.9).
Choosing the wrong denominator is the most common percent-error mistake.
- Over 100%: yes — whenever the gap is bigger than the actual value. Measured 25 against actual 10 gives |25 − 10| ÷ 10 = 150%.
- Exactly 100%: when the measured value is 0 (or double the actual, over).
- Negative: never for percent error itself — the formula uses absolute values, so error is always ≥ 0%. Direction lives in the signed difference, which this page shows separately.
If your teacher or lab manual asks for a signed percent error, drop the absolute values: (measured − actual) ÷ actual × 100.
Signed error: direction is information
Percent error is usually quoted as a positive figure, but the signed error carries information the absolute figure throws away. A measurement of 98 against a true value of 100 is a signed error of minus 2 percent; a measurement of 102 is plus 2 percent. The absolute percent error is 2 percent in both cases, yet the two instruments are failing in opposite directions, and a technician who only sees the absolute figure cannot tell whether to recalibrate up or down.
The habit to build is to record the signed difference first and the absolute figure second. Signed error answers whether the instrument reads high or low. Absolute error answers how far off it is. Percent error, properly reported, is the absolute figure with the signed figure alongside it, because a lab notebook that only records size will eventually mislead someone about direction.
Percent error vs percent difference: the one-line test
The one-line test is whether a true value exists. If there is an accepted, theoretical, or true value to compare against, the tool is percent error: the gap divided by the true value. If there are two measurements and neither is the truth, the tool is percent difference: the gap divided by the average. Applying percent error without a true value divides by an arbitrary choice, and applying percent difference to a true value wastes the one piece of ground truth the experiment has.
A school chemistry example makes the test concrete. A student measures the density of aluminium as 2.60 g per cubic centimetre against the accepted 2.70. A true value exists, so the percent error is 0.10 divided by 2.70, which is 3.70 percent. If two students measure 2.60 and 2.80 with no accepted value in play, the percent difference is 0.20 divided by 2.70, which is 7.41 percent, and neither student’s figure is privileged.
Frequently asked questions
Quick answers about this percent error calculator.
How do you calculate percent error?
Percent error = |measured − actual| ÷ |actual| × 100. Subtract, take the absolute value, divide by the actual value, and multiply by 100. Measuring 9.8 against an actual 10 gives 2.00%.
What does a 2% error mean?
Your measurement is within 2% of the accepted value — for most classroom and workshop work, that is a good result. Under 1% is excellent; over 10% usually means the method or instrument needs a look.
Why does an actual value of 0 break the formula?
Percent error divides by the actual value, and division by zero is undefined — an error of any size against a true value of 0 is infinitely large in relative terms. Use absolute error instead for zero targets.
Can percent error be negative?
No — the standard formula uses absolute values, so percent error is always zero or positive. If you need direction, look at the signed difference (measured − actual): positive means you measured high, negative means low. Or set “Percent error shown as” to Signed above and the headline percent itself keeps its sign.
What is the difference between percent error and percent difference?
Percent error divides by the accepted (actual) value and is used when a true value exists. Percent difference divides by the average of two values and is used when neither is the accepted truth.
Is percent error the same as percent accuracy?
They are complements: percent accuracy = 100% − percent error. A 2.00% error means 98.00% accuracy. Labs usually report the error; product specs often quote the accuracy.
Should percent error be positive or negative?
Percent error is usually reported as a positive figure, but the signed error should be recorded alongside it. The sign tells you whether the measurement reads high or low, which the absolute figure alone cannot show.
What is the difference between percent error and percent difference?
Percent error divides the gap by a true or accepted value; percent difference divides the gap by the average of two values. Use percent error when a true value exists, and percent difference when neither value is the truth.
What if I do not know the true value?
Then percent error does not apply, because there is nothing to divide by. Use percent difference for two measurements, or relative error against the measurement you are treating as the reference, and say which you chose.
Related calculators
More ways to check numbers and data.
Disclaimer
This calculator is for information and education only. Percent error summarizes one comparison; it does not by itself prove an instrument is calibrated or a result is valid. For regulated lab, medical, or engineering work, follow your field’s official measurement standards.