OnlineCalculator360
Result
How the Calculator Works
Enter the experimental (or estimated) value and the true (or accepted) value. The calculator computes the percentage by which your measured result deviates from the correct answer, with the sign preserved so you know whether your result was too high or too low.
The "true value" is always the reference point. In a school experiment, it is the published constant (density of water, speed of sound, etc.). In a budget context, it is the approved estimate. In a sales forecast, it is the actual revenue figure.
Formula and Worked Example
Positive result: experimental value was higher than true value (overestimate).
Negative result: experimental value was lower than true value (underestimate).
Student measured: 340 m/s. Published true value: 343 m/s.
% Error = ((340 − 343) ÷ 343) × 100 = (−3 ÷ 343) × 100 = −0.87%
The student's result was 0.87% below the accepted value. Excellent accuracy for a school lab.
Example 2: Construction cost estimate
Quantity surveyor's estimate: ₹45,00,000. Final actual cost: ₹48,60,000.
% Error = ((48,60,000 − 45,00,000) ÷ 45,00,000) × 100 = (3,60,000 ÷ 45,00,000) × 100 = +8%
The project ran 8% over the approved estimate.
Where Percentage Error Is Used
| Field | Experimental Value | True Value | What Good Looks Like |
|---|---|---|---|
| School / college lab | Measured constant | Published standard | < ±5% for most practicals |
| Construction QS | Project estimate | Final bill of quantities | < ±10% for a preliminary estimate |
| Sales forecasting | Revenue forecast | Actual revenue | < ±5% for a monthly forecast |
| Medical dosing | Calculated dose | Prescribed dose | < ±2% for IV drug preparation |
| Weather forecast | Predicted rainfall | Observed rainfall | Varies; < 15% for 24-hour forecast |
| Manufacturing QC | Measured dimension | Design specification | Within tolerance band (e.g. ±0.5%) |
Percentage Error vs Percentage Difference
These two calculations are frequently confused. The distinction is about whether one value is the "correct" reference:
| Aspect | Percentage Error | Percentage Difference |
|---|---|---|
| Reference point | One value is defined as "true" or "accepted" | Neither value is more correct than the other |
| Denominator | The true value | The average of the two values |
| Sign | Signed (positive = overestimate) | Unsigned (always positive) |
| Use case | Lab experiments, budget tracking, forecast accuracy | Comparing two vendors, two measurements, two candidates |
Frequently Asked Questions
% Error = ((Experimental − True) ÷ True) × 100. Positive means overestimation; negative means underestimation.
Percentage error requires a known true value as the denominator. Percentage difference uses the average of two values as the denominator because neither is the "correct" reference. Use percentage error when comparing to a standard; use percentage difference for neutral comparisons.
Not always. The signed version (used here) shows a negative result when the experimental value is below the true value. Some textbooks use absolute value |Experimental − True| to give an unsigned result. The signed version gives more information.
For CBSE and ISC practicals, ±5% is generally acceptable, ±2% is excellent, and above 10% warrants a review of technique or equipment calibration.
The approved estimate is the true value, and the final bill of quantities is the experimental value. If an estimate was ₹45L and the project cost ₹48.6L: % error = ((48.6 − 45) ÷ 45) × 100 = +8%. Tracking this across projects improves future estimating accuracy.
Absolute error = |Experimental − True| and has units (grams, rupees, etc.). Percentage error normalises by the true value to produce a unit-free ratio, allowing comparison across experiments with different scales.
Yes. If the experimental value is more than double the true value, the error exceeds 100%. In project management, a cost overrun from ₹10L to ₹25L would be: ((25 − 10) ÷ 10) × 100 = 150% error.
Meteorological agencies compare predicted values (temperature, rainfall) against observed values. A 40 mm rainfall forecast vs 35 mm actual: ((40 − 35) ÷ 35) × 100 = +14.3%. Tracking this over many forecasts helps improve predictive models.