Percent Error Calculator: Measured vs Accepted Value
Work out the percent error between a measured value and the accepted true value — the headline accuracy metric in chemistry labs, physics experiments, and engineering tolerances.
The measured value (95) is below the accepted value (100).
Educational estimates only. Not a substitute for certified calibration, laboratory QA/QC, engineering tolerance review, or regulatory compliance.
The formula
Percent error scales the size of a measurement’s miss against the value treated as correct:
The result is a non-negative magnitude. The signed percent error — the same expression without the absolute value in the numerator — is reported separately so direction (over vs under) is not lost.
How this calculator works
Measured (experimental) value vs accepted (true) value. The measured value is what your instrument, experiment or computation produced. The accepted value is the reference you are comparing against — a CODATA physical constant, a published reference figure, or any value treated as the truth for this comparison.
Why the absolute value. Percent error is reported as a positive magnitude because “how far off was I?” is a distance, not a direction. Taking |measured − accepted| means a reading that is 5 high and one that is 5 low both report the same 5 — the size of the miss, independent of which way it went.
Why the denominator is the accepted value. Dividing by the accepted value anchors the error to the reference point, which makes errors comparable across measurements of wildly different size. A 1-unit miss is 10% against an accepted value of 10 but only 0.1% against an accepted value of 1,000.
Magnitude vs signed direction. The headline percent error is the magnitude (always ≥ 0). The signed percent error is a separate, directional variant: it keeps the sign so you can see whether the measurement ran high (positive) or low (negative). The signed figure is a complement to the standard metric, not a replacement — the standard percent error is not itself “negative”.
Why an accepted value of zero is undefined. The formula divides by the accepted value. When that value is zero the division is undefined — there is no meaningful “percentage of nothing”, and values near zero inflate the percentage without limit. In that case report the raw difference, or switch to percent difference.
Worked example
Suppose the accepted value of the acceleration due to gravity is 9.81 m/s² and your experiment measured 9.74 m/s².
- Measurement deviation: 9.74 − 9.81 = −0.07 (the reading ran low).
- Absolute error: |−0.07| = 0.07.
- Relative error: 0.07 ÷ 9.81 = 0.007136.
- Percent error (magnitude): 0.007136 × 100 ≈ 0.7136%.
- Signed percent error: −0.07 ÷ 9.81 × 100 ≈ −0.7136% — the minus sign shows the measurement was below the accepted value.
You would quote this as a 0.7136% error, noting the measurement was slightly low. Enter these values above to see the same numbers update live.
Worked examples
Common accepted/measured pairs, every figure computed by this calculator:
| Accepted value | Measured value | Absolute error | Signed percent error | Percent error (magnitude) |
|---|---|---|---|---|
| 100 | 95 | 5 | -5% | 5% |
| 50 | 53 | 3 | +6% | 6% |
| 9.81 | 9.74 | 0.07 | -0.7136% | 0.7136% |
| 200 | 210 | 10 | +5% | 5% |
| 0 | 5 | 5 | — | Undefined |
Every figure above is produced by the same engine that powers the calculator. The final row shows the accepted-value-zero case: percent error is undefined, so only the raw difference is meaningful.
Percent error vs percent difference — which to use
The two metrics answer different questions and use different denominators. Choosing the wrong one misrepresents the quality of a measurement.
Percent error needs a reference you trust as the truth — an accepted, theoretical or certified value. It divides by that accepted value:
Percent difference is for two measurements where neither is privileged as correct — comparing two instruments, two lab teams, or two runs of the same unknown. It divides by the average of the two values’ magnitudes:
When to use which. Determining the molar mass of a known compound against a periodic-table value? The reference is the truth — use percent error. Comparing two student teams’ results for an unknown sample, where neither has privileged truth status? Use percent difference. Mixing the two misrepresents measurement quality.
Rule of thumb: if you can point to a value and say “that one is correct”, use percent error. If you cannot, use percent difference. The mode switch at the top of the calculator toggles between them.
Acceptable percent error by application
Acceptable percent error is set by the application, not by a universal rule. The example ranges below reflect commonly cited practice in each setting and are illustrative only — always check the governing standard or specification for your own work.
There is no universal “good” percent error; the acceptable value depends on the tolerance required by the application. The figures below are indicative examples of typical professional practice, not universal standards — always check the specification that governs your context.
| Setting | Example range often cited | Where to check |
|---|---|---|
| Student physics teaching lab | ≈5–10% often accepted; ≈1–2% considered strong | Course or instructor guidance |
| General analytical chemistry | ≈1–5% commonly cited | The method or SOP for the assay |
| Titration (volumetric analysis) | ≈1–3% commonly cited | The validated lab method |
| Trace analysis (e.g. ICP-MS) | ≈5–10% commonly cited | Method validation data |
| Engineering field measurement | ≈2–5% commonly cited | The project tolerance specification |
| Precision instruments / metrology | ≈0.01–0.5% commonly cited | The calibration certificate or governing standard |
| Consumer devices (kitchen scale, thermometer) | ≈2–5% typical | The manufacturer specification |
These figures are illustrative ranges, not regulatory requirements. There is no universal good percent error; the acceptable value depends on the tolerance required by the application. For any regulated or safety-critical use, verify the exact limit in the governing standard or specification rather than relying on a rule of thumb.
Report percent error with significant figures that match the precision of the measurement: quoting 100.0 ± 5% says more than 100 ± 5%, which implies the reading was only good to the nearest whole unit.
Frequently Asked Questions
Can percent error be negative?
The standard percent error is reported as a non-negative magnitude, because it answers 'how far off was the measurement?', which is a distance. This calculator also shows a separate signed percent error: that directional variant keeps the sign and can be negative (measurement below the accepted value) or positive (above). The signed figure complements the standard metric — it does not replace it.
What if the accepted value is zero?
Percent error is undefined when the accepted value is zero, because the formula divides by it. This tool fails closed: it shows 'undefined' instead of returning Infinity or NaN, and suggests reporting the raw difference or using another metric such as percent difference. Values very close to zero are also unreliable, since a tiny denominator inflates the percentage without limit.
Percent error vs percent difference — what is the difference?
Percent error needs a reference value you trust as the truth and divides by it: |measured − accepted| ÷ |accepted| × 100. Percent difference is for two values where neither is privileged as correct and divides by their average: |A − B| ÷ ((|A| + |B|) ÷ 2) × 100. Use percent error when an accepted value exists; use percent difference when it does not. The calculator has a mode switch for both.
What is a good percent error?
There is no universal good percent error; the acceptable value depends on the tolerance required by the application. As indicative examples, student physics labs often accept 5–10%, analytical chemistry frequently targets 1–3%, and precision metrology may demand better than 0.1%. Always check the standard or specification that governs your context rather than relying on a single rule of thumb.
Should I use absolute or signed percent error?
Use the absolute (magnitude) percent error as the headline figure when you only care how far off a measurement was — this is the standard convention in most lab reports. Use the signed percent error when direction matters, for example to detect a systematic bias where an instrument reads consistently high or low. Report the signed value as a clearly-labelled complement, not as a substitute for the standard metric.
When is percent difference undefined?
Percent difference is undefined when both values are zero, because its denominator is the average magnitude (|A| + |B|) / 2, which is zero only when A and B are both zero. The calculator fails closed in that case: it shows an undefined message instead of returning 0%, NaN, or Infinity. For any other pair of values the average denominator is positive and the percent difference is well defined.
References & Authoritative Sources
- National Institute of Standards and Technology (NIST) — Guidelines for Evaluating and Expressing Uncertainty in Measurement · consulted June 1, 2026 · Official U.S. methodology for measurement uncertainty in scientific and industrial measurement
- CODATA — Internationally Recommended Values of Fundamental Constants — CODATA Recommended Values of the Fundamental Physical Constants · consulted June 1, 2026 · The international reference values for physical constants — the canonical 'accepted values' in physics education
Related Calculators
Methodology & Review
Percent error equals |experimental value − accepted value| / |accepted value| × 100. The calculator returns the percent error as a positive number — direction (over vs under) is sometimes meaningful in physics / chemistry experiments but the magnitude is the headline metric. The 'accepted value' is the theoretical, true, or reference value (e.g., a CODATA physical constant, a published reference measurement); the 'experimental value' is the measured or computed value. Percent error is the standard metric in laboratory science and engineering for quantifying measurement accuracy against a known reference, and is heavily used in chemistry, physics, and statistics coursework. RELIABILITY: Reliable when the 'accepted value' is genuinely the true reference. Unreliable when the accepted value is itself uncertain or itself an estimate (in that case, use percent difference instead), when comparing two equally-valid measurements neither of which is the 'truth', or when accepted value is near zero (small denominator inflates percent error). Percent difference mode uses the average magnitude denominator ((|A| + |B|) / 2) and is undefined when both inputs are zero.
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