Calculate the percent error between your experimental (measured) value and the theoretical (accepted) value — with signed or unsigned result, accuracy rating, and full step-by-step working.
Enter your measured (experimental) value and the accepted (theoretical) value. The calculator will show your % error and an accuracy rating.
Percent error measures how close an experimental (measured) result is to the theoretically expected or accepted value — expressed as a percentage of the theoretical value. It is the standard accuracy metric used in chemistry, physics, biology, and engineering labs worldwide. A small percent error means your measurement is highly accurate; a large one signals significant deviation from the expected result.
Unlike percentage difference — which treats both values equally — percent error has a clear asymmetry: one value is the known correct reference (theoretical), and the other is your measurement (experimental). The theoretical value always goes in the denominator.
% Error = (|Experimental − Theoretical| ÷ |Theoretical|) × 100
The absolute value bars | | ensure the result is always positive — you only care about how far off you were, not which direction.
% Error = ((Experimental − Theoretical) ÷ |Theoretical|) × 100
Positive = your measurement was higher than expected (overestimate). Negative = your measurement was lower than expected (underestimate).
Experimental value: 0.985 g/mL | Theoretical value: 1.000 g/mL
Step 1 — Difference: |0.985 − 1.000| = 0.015
Step 2 — Divide: 0.015 ÷ 1.000 = 0.015
Step 3 — Multiply: 0.015 × 100 = 1.5% error
Verdict: ✅ Excellent — well within the accepted <5% lab threshold.
Experimental value: 9.4 m/s² | Theoretical value: 9.81 m/s²
Step 1 — Difference: |9.4 − 9.81| = 0.41
Step 2 — Divide: 0.41 ÷ 9.81 = 0.0418
Step 3 — Multiply: 0.0418 × 100 = 4.18% error
Signed direction: Experimental < Theoretical → underestimate (−4.18% signed)
The acceptable percent error threshold depends on the context — equipment precision, the nature of the experiment, and the level of education. Here are common benchmarks:
Professional analytical chemistry and industrial quality control labs often require percent errors under 1–2%. Physics experiments involving fundamental constants may have published acceptable error ranges of 0.1–0.5%. Always check your instructor's or organisation's specified threshold.
Always positive. Tells you how much you were off. Used in most school labs, textbooks, and standard reports. Formula uses |absolute value| of the difference.
Can be positive (overestimate) or negative (underestimate). Useful in science research to identify systematic bias — whether your method consistently measures too high or too low.
| Formula | Denominator | Direction? | Use When |
|---|---|---|---|
| Percent Error | |Theoretical value| | Optional (signed/unsigned) | Measured vs known correct value |
| % Difference | Average of both values | No — always positive | Two independent equal-standing values |
| % Change | Old (original) value | Yes — + increase / − decrease | Before-and-after time comparison |
| Experiment | Experimental | Theoretical | % Error | Rating |
|---|---|---|---|---|
| Density of aluminium | 2.64 g/cm³ | 2.70 g/cm³ | 2.22% | Excellent |
| Boiling point of ethanol | 76.5°C | 78.4°C | 2.42% | Excellent |
| Gravitational acceleration | 9.4 m/s² | 9.81 m/s² | 4.18% | Acceptable |
| Speed of sound (room temp) | 360 m/s | 343 m/s | 4.96% | Borderline |
| π approximation (22/7) | 3.1429 | 3.14159 | 0.04% | Excellent |
| Molar mass experiment | 44.5 g/mol | 44.0 g/mol | 1.14% | Excellent |
| Resistance (Ohm's Law lab) | 52 Ω | 47 Ω | 10.64% | High Error |
Understanding why your percent error is high is as important as calculating it. Common sources of experimental error include:
Common questions about calculating and interpreting percent error
% Error = (|Experimental − Theoretical| ÷ |Theoretical|) × 100. Subtract the theoretical value from the experimental value, take the absolute value, divide by the absolute theoretical value, and multiply by 100. The theoretical value always goes in the denominator — never the experimental one.
In most school and university labs, a percent error under 5% is considered acceptable. Professional analytical labs often require under 1–2%. The threshold depends on the experiment, equipment used, and your instructor's requirements. Use the accuracy scale in our calculator above to see where your result lands.
Standard (unsigned) percent error is always positive. However, signed percent error can be negative — a negative result means your experimental value was lower than the theoretical value (an underestimate). A positive signed error means your measurement was higher (an overestimate). Toggle "Signed" mode in the calculator above to get a directional result.
The theoretical value is the accepted correct reference — the standard you are comparing against. Dividing by it measures the error as a fraction of what the result should have been. Dividing by the experimental value would be meaningless in context, since the experimental value is the one that contains the error.
Percent error has one value designated as the accepted/correct reference (theoretical) and divides by it. Percent difference treats both values as equal, has no reference standard, and divides by their average — making the result symmetric. Use percent error when one value is a known correct standard; use percent difference when both values are independent observations.
Yes — percent error can exceed 100% if the experimental value is more than double (or nearly zero compared to) the theoretical value. For example: experimental = 25, theoretical = 10 → % error = (|25−10| ÷ 10) × 100 = 150%. This is mathematically valid, though it indicates a very significant measurement error in practice.
Key strategies: (1) Calibrate all instruments before use. (2) Take multiple readings and average them to reduce random errors. (3) Control environmental variables like temperature and humidity. (4) Use higher-precision equipment where possible. (5) Identify and eliminate sources of systematic bias — if your signed error is consistently negative, your method is systematically underestimating.
Percent error is mathematically undefined when the theoretical value is zero — because you would be dividing by zero. In such cases, use absolute error (simply the difference between the two values) rather than percent error. Our calculator will flag this scenario and display an error message asking for a non-zero theoretical value.