Percentages appear everywhere — grades, discounts, taxes, statistics — yet the underlying formulas are often forgotten because the calculations feel intuitive but the exact steps aren't. Here's a clear breakdown.
To find what percentage one number is of another, divide the part by the whole and multiply by 100:
Percentage = (Part ÷ Whole) × 100
For example, if you scored 42 out of 50 on a test: (42 ÷ 50) × 100 = 84%.
To find, say, 20% of 150, convert the percentage to a decimal (0.20) and multiply: 0.20 × 150 = 30.
To calculate a percentage increase, subtract the original value from the new value, divide by the original value, then multiply by 100:
% Increase = ((New − Original) ÷ Original) × 100
The formula for a percentage decrease works the same way, except the result will be negative, indicating a drop rather than a rise.
These two terms are commonly confused. If an interest rate moves from 5% to 8%, that's a rise of 3 percentage points, but a 60% percentage change relative to the original rate ((8−5)/5 × 100). Financial news often mixes these up, so it's worth double-checking which one is being reported.
A jacket costs Rs. 4,000, is on a 25% discount, and has 5% sales tax applied after the discount. First, apply the discount: 4,000 × (1 − 0.25) = 4,000 × 0.75 = Rs. 3,000. Then apply tax on the discounted price: 3,000 × 1.05 = Rs. 3,150. A common mistake is applying both percentages to the original price separately and adding/subtracting them — this gives a different (and incorrect) final answer, because tax is calculated on the already-discounted price, not the original price.
In physics and chemistry practicals, percentage error measures how far an experimental result is from the accepted/theoretical value: % Error = (|Experimental − Theoretical| ÷ Theoretical) × 100. For example, if you measure the acceleration due to gravity as 9.7 m/s² but the accepted value is 9.8 m/s², the percentage error is (0.1 ÷ 9.8) × 100 ≈ 1.02%. Lab reports usually expect this calculation explicitly, along with a brief comment on likely sources of error.
Why doesn't a 20% increase followed by a 20% decrease return to the original value?
Because the second percentage is applied to a different number. If you start with 100, a 20% increase gives 120, but a 20% decrease from 120 is 24, leaving you at 96 — not back at 100. Percentages are always relative to whatever base value they're applied to at that moment.
What's the difference between percentage change and percentage error?
Percentage change compares two values to see how much something has moved (increase or decrease), while percentage error specifically compares an experimental or measured value against a known correct/theoretical value, to judge measurement accuracy.
Calvo's percentage calculator handles all of these cases instantly — basic percentages, increases, decreases, percentage-point differences, and multi-step calculations like discount-plus-tax — without needing to track intermediate values by hand.
Try every formula from this guide in the free Percentage Calculator. No sign-up needed.