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Percent Error Formula
The percent error formula is the absolute value of the difference between the measured and actual values divided by the actual value and multiplied by 100.
As the name implies, percent error is the difference in percentage form between an item’s precise or known value and its approximate or measured value. It is used to report the difference between the experimental value and its real or exact value in scientific experiments.
A percent mistake shows how far off you are from the precise amount when estimating the value of something.
These errors may occur due to equipment imprecision, measurement (human or tool error), or adjustments made to computation procedures (rounding off, etc.).
Formula:
(Approximate or experimental Value – Exact or known Value/Exact or known Value) × 100 = percent error
Solved Examples:
Q1. The study stated that the garage could accommodate 220 vehicles, but we only found 200 parking places. What is the percentage error in the report?
Percent Error = [|220 − 200| / 200] × 100%
= [20/200] × 100%
= 0.1 × 100% = 10%
This report contains a 10% error.
Q2. A man set up a stall expecting to receive 80 visitors every day, but only 60 people showed up each day. Determine the percentage inaccuracy.
The estimated value is = 100
The original value is = 80
Thus, percentage error = [80-60] / 60 × 100%
= 20/60 × 100 %
= ⅓ × 100 %
= 33.33 %
Percentage inaccuracy is 33.33 %
Q3. Due to certain minor mistakes, a scale incorrectly measures a value of 8 cm. If the actual measurement of the value is 12 cm, calculate the percentage inaccuracy.
It is given that,
Approximate value = 8 cm
Exact value = 12 cm
Percentage Error = (Approximate Value – Exact Value / Exact Value) × 100
Percentage Error = (8 – 12)/12 × 100
= -33.3%
