Percentage Calculator
Work out what P% of a number is, what percent one number is of another, the percentage change between two values, or the original value before a percentage increase or decrease — with the working shown for each.
The four percentage formulas
- P% of X: 18.5% of 450 = 0.185 × 450 = 83.25.
- X is what % of Y: 30 of 120 = 30 ÷ 120 × 100 = 25%.
- Percent change: 80 to 100 = (100 − 80) ÷ 80 × 100 = 25%.
- Reverse percent: $120 after 20% off = 120 ÷ 0.80 = $150.
Written by Suhaib Hassan. Each formula and worked example is re-derived by hand before publishing. Our methodology.
It converts a percentage to a fraction of 100, scales the base by that fraction, and for the reverse problems divides by the growth factor (1 ± rate).
Percent questions come in four shapes that are easy to mix up. Pick the one you have and see the answer, the fraction and the multiplier together.
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Step-by-step working
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The three ideas behind every percentage problem
1. Percent means “per hundred”
P% is the fraction P ÷ 100. To find a portion, scale the base by that fraction.
Y = 0.185 × 450 = 83.25
Check: 83.25 ÷ 450 × 100 = 18.5% ✓
2. Increases and decreases are not symmetrical
Percentage change is measured against the starting value, so undoing a change needs a different percentage.
150 → −50% → 75 (not 100)
To return: 150 → 100 is −33.33%
3. Reverse percentages divide, not subtract
To recover the original before a change, divide the final value by the growth factor.
X = Final ÷ (1 ± r)
$120 after 20% off: 120 ÷ 0.80 = $150
Worked examples
Illustrative figures, each checked by hand.
Markup vs margin
A retailer adds a 30% markup to a $100 cost, giving a $130 price.
Margin = 30 ÷ 130 = 23.08% of price
The same $30 profit is a different percentage depending on the base.
Real pay after inflation
A wage rises 3.0% while prices rise 4.5%.
= −1.44% (about)
Dividing growth factors is more accurate than subtracting 4.5 from 3.0.
Discount, then tax
An $80 item is 25% off and then 8% sales tax is added.
60.00 × 1.08 = $64.80
Tax is calculated on the discounted price, so the order matters only if the store applies them differently.
What is a percentage?
A percentage is a number expressed as a fraction of 100. “18.5%” means 18.5 out of every 100, or 0.185. Percentages make it easy to compare parts of wholes of different sizes.
The four formulas
- P% of X: Y = (P ÷ 100) × X
- X is what % of Y: % = (X ÷ Y) × 100
- Percentage change: % change = (new − old) ÷ |old| × 100
- Reverse percentage: original = final ÷ (1 ± rate ÷ 100), using + for an increase and − for a decrease
By Suhaib Hassan · Reviewed 28 September 2026 · How CalculatePilot verifies formulas →
Sources
- NIST Special Publication 811, Guide for the Use of the International System of Units (SI) — treatment of the percent sign and dimensionless quantities.
- ISO 80000-2:2019, Quantities and units — Part 2: Mathematics.
Frequently asked questions
Why aren’t percentage increases and decreases symmetrical?
Percentage change is measured against the starting value. Going from 100 to 125 is +25%; going from 125 back to 100 is −25 ÷ 125 = −20%, because the base is now 125. A 25% increase therefore needs a 20% decrease to return to the original.
What is the difference between percentage points and percent change?
Percentage points are the simple difference between two percentages: going from 4% to 5% is 1 percentage point. Percent change compares them proportionally: 5 is 25% more than 4. Mixing the two up is a common source of misleading headlines.
How do I calculate a discount before sales tax?
Multiply the price by (1 − discount rate) to get the sale price, then multiply by (1 + tax rate). For $80 with 25% off and 8% tax: 80 × 0.75 × 1.08 = $64.80. Some jurisdictions tax the pre-discount price in certain cases, so check the local rules.
How do I find the original price before a percentage change?
Divide the final value by the growth factor. After a 20% discount the factor is 0.80, so a $120 price came from 120 ÷ 0.80 = $150. Subtracting 20% of $120 would give the wrong answer.
Can a percentage be greater than 100%?
Yes. 150% of a number is one and a half times it, and a value that doubles has increased by 100%. Only percentages of a fixed whole (such as a share of a total) are limited to 100%.
What if the starting value is zero?
Percentage change from zero is undefined because it divides by zero, and “X is what percent of 0” is undefined for the same reason. Report the absolute change instead.
How percentages, increases and “what percent” questions are worked out: percentage calculator guide.
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