Percent Error

1. Enter your **Experimental Value** — the number you measured or recorded in your experiment.
2. Enter the **Theoretical Value** — the accepted or expected true value (e.g., a known physical constant, textbook value, or standard reference).
3. Click **Calculate** to instantly compute the percent error.
4. Read your result: a small percent error (close to 0%) means high accuracy; a large percent error means significant deviation from the true value.
5. Use the step-by-step breakdown shown below the result to understand exactly how the calculation was performed.

Percent Error (%) = (|Experimental Value − Theoretical Value| / |Theoretical Value|) × 100

• Experimental Value (E) — The value you measured or obtained through your experiment or observation.
• Theoretical Value (T) — The accepted, known, or true value you are comparing against (e.g., a textbook constant or standard reference value).
• |…| — Absolute value — ensures the result is positive regardless of whether the experimental value is above or below the theoretical value.
• Percent Error (%) — The final output: how much the experimental value differs from the theoretical value, expressed as a percentage.

Step 1 — Difference: |2.85 − 2.70| = 0.15
Step 2 — Divide by theoretical: 0.15 / 2.70 ≈ 0.05556
Step 3 — Multiply by 100: 0.05556 × 100 ≈ 5.56%

Result: Percent Error ≈ 5.56%

A percent error of 5.56% means your experimental measurement of aluminum's density was about 5.56% higher than the accepted value of 2.70 g/cm³. In most high-school and undergraduate labs, a percent error under 5% is considered acceptable, so a 5.56% error is slightly outside that threshold — suggesting a small but notable source of experimental error, such as impure samples or measurement instrument inaccuracy.

What Is Percent Error?

Percent error is a standard way to quantify the accuracy of an experimental result compared to a known or accepted value. It is widely used in physics, chemistry, biology, and engineering labs.

Why Use Absolute Value?

The absolute value in the formula means percent error is always expressed as a non-negative number. This reflects the size of the deviation without regard to direction (above or below). If you need to track whether your value is too high or too low, you can note the sign separately, but the classical percent error formula is unsigned.

Interpreting Your Result

| Percent Error | Interpretation | |---|---| | 0% | Perfect match — experimental equals theoretical | | < 5% | Generally acceptable in most lab settings | | 5–10% | Moderate error; review your procedure | | > 10% | Significant error; likely a procedural or equipment issue |

(Acceptable thresholds vary by discipline and context — always check your instructor's or industry's standard.)

Percent Error vs. Percent Difference

Percent error compares a single measured value to a known theoretical value. Percent difference compares two experimental values when neither is considered the 'true' value — it uses the average of the two numbers in the denominator instead.

Common Applications

• Science labs: Verifying experimental measurements against physical constants (e.g., speed of light, density of elements).
• Manufacturing: Quality control — checking whether produced parts fall within tolerance.
• Finance: Comparing forecasted vs. actual figures (though different terminology is typically used).
• Education: Teaching students about measurement uncertainty and experimental accuracy.

• **Using the experimental value in the denominator** instead of the theoretical (accepted) value — always divide by the theoretical value.
• **Forgetting the absolute value** — without it, your result could be negative, which misrepresents the magnitude of error.
• **Confusing percent error with percent difference** — use percent error only when one value is the known true/accepted value.
• **Using inconsistent units** — make sure both your experimental and theoretical values are in the same units before subtracting.
• **Interpreting a negative experimental difference as 'less accurate'** — accuracy depends on the magnitude, not the direction, of the deviation.

• Measurement and Uncertainty — Physics Lab Resources — NIST (National Institute of Standards and Technology)
• NIST/SEMATECH e-Handbook of Statistical Methods: Accuracy and Precision — NIST (National Institute of Standards and Technology)

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