A 15% tip on a bill of 80
15 ÷ 100 = 0.15, and 0.15 × 80 = 12. The tip is 12 and the total is 92.
Notice that 15% of 80 equals 80% of 15. Swapping the two numbers never changes the answer, which is often the faster way to do it in your head.
Percentage calculator
Four percentage questions, one calculator. Pick the one you are asking, enter your numbers, and read the answer with the working written out underneath.
Result
Fill in the fields to see your result.
How it works
A percentage is a fraction whose denominator is fixed at 100. That single idea covers every calculation here: 25% is just another way of writing 25/100, or the factor 0.25. Once a percentage has become a factor, working with it is ordinary arithmetic — multiply to apply it, divide to undo it.
The one place people go wrong is the base. A percentage is always a percentage *of* something, and changing that something changes the answer. Going from 100 to 125 is a 25% increase; going back from 125 to 100 is a 20% decrease. Both moves are 25 units, but they are measured against different starting numbers.
The same trap explains why percentages do not add. Two successive rises of 10% multiply — 1.10 × 1.10 = 1.21 — so the total is 21%, not 20%. This calculator shows the multiplier for exactly that reason: once you think in multipliers, chained percentages stop being surprising.
Formulas used
Percentage of a number
result = (p ÷ 100) × n
- p
- the percentage
- n
- the number it applies to
Percentage change
change = (new − old) ÷ |old| × 100
The absolute value in the denominator keeps the sign of the change meaningful when the starting number is negative.
Worked examples
A price rising from 120 to 150
The difference is 30. Compared with the starting price of 120, that is 30 ÷ 120 = 0.25, or a 25% increase. The multiplier is 1.25.
Going back from 150 to 120 is a 20% decrease, not 25%. The move is the same size, but it is now measured against 150.
Assumptions and limits
- Percentage change is measured against the absolute value of the starting number, so the sign of the result reflects the direction of the move.
- Results are shown to six significant decimals; the underlying calculation keeps full precision.
- The fraction is only offered when both numbers are whole, since that is the only case where it is exact.
Frequently asked questions
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages; percent measures a relative change. If an interest rate moves from 4% to 5%, that is a rise of one percentage point and an increase of 25%.
Newspapers mix the two constantly. When a figure sounds surprisingly large, check which one is being used.
Why does a 20% discount followed by a 10% discount not make 30%?
Because the second discount applies to the already-reduced price. The multipliers combine: 0.80 × 0.90 = 0.72, so the final price is 72% of the original and the real discount is 28%.
Stacked percentages always multiply. They only add when each one is applied to the same original base.
How do I remove a percentage that has already been added?
Divide rather than subtract. If a price of 120 includes 20% tax, the pre-tax price is 120 ÷ 1.20 = 100, not 120 − 24 = 96. Subtracting 20% takes 20% of the wrong number.
Can a percentage be greater than 100?
Yes, whenever the part is larger than the whole. Sales of 150 against a target of 100 are 150% of target. Percentages above 100 only look odd when the whole is genuinely a maximum, such as a share of a fixed total.
Updated
Related calculators
Fractions Add, subtract, multiply and divide fractions, reduce them to lowest terms, and convert between fractions and decimals. Ratios Simplify a ratio, share a total between any number of parts, or solve a proportion by cross multiplication. Discount Find the sale price, the percentage off, or the price before the discount — including stacked offers and sales tax. Statistics Paste a series of numbers and read its mean, median, spread, quartiles, skewness and outliers at a glance.