Percent Error Calculator
Measured vs. theoretical value → percent error, absolute error, signed error, full step-by-step working, and a lab-style accuracy reading. 100% client-side.
Percent Error = |E − T| ÷ |T| × 100%
Result
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Absolute error |E−T|
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Signed error
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Direction
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Step by step
Not what you need? This tool divides by the theoretical value — it is directional.
If neither of your two numbers is the "true" one, you want
percent difference instead (divides by the average — symmetric).
See the full comparison below.
Percent error vs. percent difference
| Percent error (this tool) | Percent difference | |
|---|---|---|
| Formula | |E−T| ÷ |T| × 100% | |a−b| ÷ ((a+b)/2) × 100% |
| Denominator | Theoretical / accepted value | Average of both values |
| Symmetric? | No — swapping E and T changes the answer | Yes — swapping a and b gives the same answer |
| Use when | You have a known true value (lab, physics, chemistry) | Comparing two measurements with no reference value |
| Example | Measured 4.9 vs accepted 5.0 → 2% | Reading 4.9 vs reading 5.1 → 4% |
Worked example
Lab report: you measured 10 g; the accepted value is 8 g.
- Subtract: 10 − 8 = 2
- Absolute error: |2| = 2
- Divide by |T|: 2 ÷ 8 = 0.25
- × 100%: 0.25 × 100 = 25%
Signed error is +25% → an overestimate (you measured too high). Accuracy reading: large error (>10%).
Accuracy guide
| Percent error | Reading |
|---|---|
| ≤ 1% | Excellent accuracy — lab-grade result |
| ≤ 5% | Good accuracy — solid for most lab and field work |
| ≤ 10% | Moderate error — fine for rough work, review your procedure |
| > 10% | Large error — check procedure, equipment, and units |
Frequently asked questions
What is the percent error formula?
Percent error = |experimental − theoretical| ÷ |theoretical| × 100%. Worked example: measured 4.9 vs theoretical 5.0 → |4.9 − 5.0| = 0.1, 0.1 ÷ 5.0 = 0.02, 0.02 × 100 = 2% percent error.
What is the difference between percent error and percent difference?
They use different denominators. Percent error divides by the theoretical (accepted) value: |E−T|/|T|×100 — it is directional and needs a known true value. Percent difference divides by the average of both values: |a−b|/((a+b)/2)×100 — it is symmetric and used when neither value is the reference. Example: measuring 4.9 against an accepted 5.0 gives 2% percent error; comparing two readings 4.9 and 5.1 with no accepted value gives 4% percent difference. Use our percent difference calculator for the symmetric version: https://nrtechstudio.com/tools/percent-difference-calculator/
Can percent error be negative?
Percent error itself is never negative because of the absolute value in |E−T|. The signed error can be negative: measured 4.9 vs theoretical 5.0 has a signed error of −2%, meaning you underestimated (measured too low). Measured 10 vs theoretical 8 has a signed error of +25%, meaning you overestimated (measured too high).
What if the theoretical value is 0?
Percent error is undefined when the theoretical value is 0, because you would divide by zero. A calculator that shows 0%, NaN, or Infinity there is lying. The absolute error |E − T| is still meaningful (for example, measured 5 vs theoretical 0 gives an absolute error of 5).
What is a good percent error?
A common lab convention: within 1% is excellent, within 5% is good, within 10% is moderate, and over 10% is a large error that deserves a second look at the procedure, equipment, or units. These are rules of thumb, not physics — strictness depends on your field.
How do I calculate percent error for a lab report?
Follow four steps. Example: you measured 10 and the accepted value is 8. Step 1: subtract, 10 − 8 = 2. Step 2: take the absolute error, |2| = 2. Step 3: divide by the absolute theoretical value, 2 ÷ 8 = 0.25. Step 4: multiply by 100, 0.25 × 100 = 25%. Report: 25% percent error (overestimate, since the signed error is +25%).
What is the difference between absolute error and percent error?
Absolute error is the raw distance |E − T| in the original units (for example, 0.1 g for measured 4.9 g vs accepted 5.0 g). Percent error divides that by |T| and multiplies by 100, giving 2% — a scale-free number you can compare across experiments of different sizes.
Does the order of the two values matter?
Yes — percent error is directional, so swapping changes the answer. Measured 10 vs theoretical 8 gives 25% (|10−8|/8×100). Measured 8 vs theoretical 10 gives 20% (|8−10|/10×100). Always put the measured value first and the accepted (theoretical) value second.
Free tool by NRTechStudio