Percentages are simple arithmetic that go wrong constantly, because four different questions all get called "the percentage". This calculator asks which one you mean — a share of a total, one number as a proportion of another, the change between two values, or working a total back from a percentage — and answers exactly that.
The four calculations
Pick the sentence that matches your question; the labels change to match.
- What is P% of X? — a discount, a tip, a tax. 20% of 80 is 16.
- X is what percent of Y? — a share or a completion rate. 30 out of 200 is 15%.
- Change from X to Y — growth or decline between two figures. From 100 to 150 is +50%.
- X is P% of what? — reversing a percentage. If 30 is 15% of something, that something is 200.
Why +20% then −20% does not get you back
Raise 100 by 20% and you get 120. Take 20% off that and you get 96, not 100. The increase is calculated on 100 and the decrease on 120, so the second percentage is a slice of a bigger cake.
This is behind a lot of misleading pricing. A price raised 25% and then advertised as "25% off" is not back to where it started — it is 6.25% below the original. To reverse a 20% increase you need a 16.67% decrease.
Percent versus percentage point
If a rate goes from 4% to 5%, that is a rise of one percentage point — but a 25% increase. Both statements are true and they describe the same change.
Reports exploit the ambiguity in both directions: the larger-sounding figure is chosen when the change should look dramatic, the smaller when it should look modest. When you read a percentage change of something that is itself a percentage, check which is meant.
Change from zero
Growth from zero to any number has no meaningful percentage. Going from 0 to 10 sales is infinite growth in percentage terms, which is why this calculator declines rather than printing a number.
Report the absolute change instead. "From 0 to 10" is informative; "an increase of ∞%" is not.
FAQ
How do I work out a percentage discount?
Use "What is P% of X?" with the discount as the percentage and the original price as the total — that gives the amount you save. Subtract it from the price for what you pay, or use 80% of the price directly for a 20% discount.
How do I remove VAT from a gross price?
Use "X is P% of what?" with the gross price as the value and 119 as the percentage for 19% VAT. That recovers the net price. Dividing by 1.19 gives the same answer.
Why does a percentage change from a negative number look strange?
This calculator divides by the absolute starting value, so going from −100 to −50 reports +50% — an improvement, which is what most people mean. Some tools report −50% for the same change. Percentage change on values that cross or sit below zero is genuinely ambiguous; prefer absolute figures there.
Is the calculation done on a server?
No. It runs in your browser and nothing is transmitted, so figures from a payslip or an invoice stay on your device.