Percent discrepancy measures how far apart two values are, expressed as a percentage. The exact formula depends on whether you’re comparing a measured value to a known standard or comparing two measurements to each other. Both versions follow the same logic: find the difference, divide by a reference value, and multiply by 100.
Two Formulas for Two Situations
The term “percent discrepancy” gets used in two distinct ways, and picking the wrong formula is one of the most common mistakes in lab reports and coursework.
When you have a known or accepted value (a textbook constant, a manufacturer’s specification, a theoretical prediction), you calculate percent error:
Percent Error = (|Measured Value − Accepted Value| ÷ Accepted Value) × 100
When you’re comparing two experimental values and neither one is “correct,” you calculate percent difference. This version uses the average of the two values as the denominator:
Percent Difference = (|Value 1 − Value 2| ÷ ((Value 1 + Value 2) ÷ 2)) × 100
The absolute value bars (the | symbols) ensure your result is always positive. You’re measuring the size of the gap, not which direction it goes.
Step-by-Step Percent Error Calculation
This is the version you’ll use most often in chemistry, physics, and engineering courses. Walk through it in five steps:
- Step 1: Subtract the accepted value from your measured value.
- Step 2: Take the absolute value of that result (drop any negative sign).
- Step 3: Divide by the accepted value.
- Step 4: Multiply by 100.
- Step 5: Write your answer with a percent sign.
Here’s a concrete example. Suppose you measure the density of aluminum in a lab and get 2.45 g/cm³. The accepted density is 2.70 g/cm³.
First, subtract: 2.45 − 2.70 = −0.25. Take the absolute value: 0.25. Divide by the accepted value: 0.25 ÷ 2.70 = 0.0926. Multiply by 100: 9.26%. Your measurement was about 9.3% off from the known density of aluminum.
Step-by-Step Percent Difference Calculation
Use this version when you ran two trials of the same experiment and want to know how consistent your results were, or when two methods give you different numbers and there’s no “correct” answer to compare against.
Say you measured the speed of a cart on a track twice and got 3.2 m/s on the first run and 3.5 m/s on the second. Subtract: 3.5 − 3.2 = 0.3. Find the average of the two values: (3.2 + 3.5) ÷ 2 = 3.35. Divide the difference by the average: 0.3 ÷ 3.35 = 0.0896. Multiply by 100: 8.96%. Your two trials differed by about 9%.
How to Do It in a Spreadsheet
If you’re working with a large data set, you can automate the calculation in Excel or Google Sheets. Put your accepted (or known) value in column A and your measured value in column B. Then type this formula into column C:
=ABS((A2-B2)/A2)*100
The ABS function handles the absolute value for you, so you don’t need to worry about negative results. For percent difference between two experimental values, adjust the denominator to the average: =ABS((A2-B2)/((A2+B2)/2))*100. Copy the formula down the column and every row calculates instantly.
What Counts as an Acceptable Result
There’s no single universal threshold. What’s “good” depends entirely on your field and the precision of your equipment.
In an introductory physics or chemistry lab, most instructors consider anything under 5% to be solid, and results under 10% are generally acceptable for basic equipment like rulers, balances, and stopwatches. Discrepancies above 10 to 15% usually signal a systematic error, not just normal measurement variation.
In clinical laboratory testing, the standards are far tighter. When hospitals evaluate whether a new testing method can replace an existing one, at least 95% of paired results need to fall within narrowly defined agreement limits. A difference that seems tiny in a classroom setting could affect a medical decision.
In inventory management, businesses use a related formula to track how closely their records match physical stock counts. If a warehouse system shows 1,000 units but a manual count finds 970, the discrepancy is 30 ÷ 1,000 = 3%, giving an inventory accuracy rate of 97%. Most supply chain professionals aim for accuracy rates above 95%.
Common Mistakes to Avoid
The most frequent error is dividing by the wrong number. In percent error, you always divide by the accepted value, not your measured value. In percent difference, you divide by the average. Swapping the denominator will change your answer, sometimes significantly, especially when the two values are far apart.
Forgetting the absolute value is another common slip. If your measured value is smaller than the accepted value, straight subtraction gives you a negative number. Percent discrepancy is always reported as a positive value because it represents the magnitude of the gap.
A subtler mistake involves comparing percentages calculated from different base values. A 5% discrepancy in one experiment and a 5% discrepancy in another don’t necessarily represent the same size error if the reference values are very different. A 5% error on a measurement of 10 is an absolute difference of 0.5, while a 5% error on a measurement of 1,000 is an absolute difference of 50. Always consider the actual numbers behind the percentage, not just the percentage itself.
Finally, watch for rounding too early. If you round intermediate steps before finishing the calculation, errors compound. Carry at least one or two extra decimal places through the division step, then round your final percentage to the appropriate number of significant figures.