Percent error

Also called Percentage error

Percent error is the difference between a measured value and an accepted value, divided by the accepted value and expressed as a percentage. It requires a known reference value, which is what separates it from percent difference.

The calculation:

\text{percent error} = \left|\frac{\text{measured} - \text{accepted}}{\text{accepted}}\right| \times 100\%

Measure the acceleration due to gravity as $9.5\ \text{m/s}^2$ against the accepted $9.8\ \text{m/s}^2$ and you have $0.3/9.8 = 0.031$ , so 3.1 percent. The denominator is the accepted value, not your measurement, and not the difference.

Percent difference is a different quantity for a different situation. When you have two measurements and no authority to prefer either, compare them against their own mean:

\text{percent difference} = \left|\frac{A - B}{(A+B)/2}\right| \times 100\%

Use percent error when a reference value exists, such as $g$ , the density of water, or the speed of light. Use percent difference when comparing two of your own results, which is the situation the AP Physics 1 CED describes when it suggests running a second experiment on the same quantity and checking the two for consistency.

The AP Physics 2 CED asks that students make a reasoned estimate of the percent error or percent difference where appropriate, and go on to say which sources of uncertainty contributed. Neither formula is printed on any AP equation sheet, so both have to be memorised.

For why the accepted value of $g$ is itself contested on this exam, see Is g 9.8 or 10.

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