Overview
Percentages are the native language of money and statistics — discounts, tips, interest, growth, grades — yet most people reach for a calculator app and then fumble the formula. This page splits the job into the three questions people genuinely ask, each with its own pair of boxes and its own live answer.
Each mode explains itself: sensible defaults show what it is for, direction labels say whether a change is an increase or a decrease, and floating-point dust like 22.49999999% is trimmed before you ever see it. Switching modes keeps your numbers, so comparing scenarios is painless.
The three percentage questions
Almost every percentage problem is one of three shapes. “What is” asks for a slice of a number — 20% of 85 is 17, the tip-and-discount shape. “What share” asks what fraction one number is of another — 17 out of 85 is 20%, the grade-and-poll shape. “What changed” compares two values over time — 85 to 102 is a 20% rise, the growth-and-inflation shape.
The classic trap is the third shape: a 50% fall followed by a 50% rise does not return you to the start, because the second percentage applies to the smaller base. Keeping the three shapes separate — as this tool does — is the simplest defence against that confusion.
Features
- Three dedicated modes with their own inputs — no mode confusion.
- Live answers updating with every keystroke.
- Direction labels on change mode: increase, decrease or flat.
- Clean decimals: floating-point dust is trimmed automatically.
- Self-explaining defaults so each mode's purpose is obvious.
- Numbers persist when switching between modes.
- Zero clutter: two boxes and an answer per mode.
- Private: all arithmetic stays in your browser.
Benefits
- The right shape, instantly. Pick the question, get the answer.
- No formula recall. The page does the structuring for you.
- Clean numbers. No 22.49999999% artefacts.
- Compare freely. Switch modes without retyping.
Who can use it
Shoppers checking discounts, diners splitting bills and tips, students working out grades, small-business owners reading growth figures, and anyone who has ever stared at “was 80, now 60” and reached for their phone. Teachers get a clean demo of why percent change is asymmetric.
How to use
- Choose the mode matching your question: of, share, or change.
- Enter the two numbers in the labelled boxes.
- Read the live answer as you type.
- On change mode, note the increase/decrease direction label.
- Switch modes freely — your numbers are kept.
Frequently asked questions
Why does a 50% drop need a 100% rise to recover?
Because the base changes. Fall 50% from 100 and you are at 50; to get back to 100 you must add 50, which is 100% of where you now stand. Percentages always apply to their starting point, so symmetric-sounding moves are asymmetric in effect. This is the single most useful thing to internalise about percentages.
What is the difference between percent and percentage points?
A rise from 20% to 25% is a 5-percentage-point rise, but a 25% relative increase (5 is 25% of 20). News headlines sometimes blur the two, and the distinction matters enormously in polls, interest rates and election coverage. When someone says “up by 5%”, always ask: five percent of what? Whenever someone quotes a change in percent, always ask: five percent of what?
How do I work out a discount in my head?
Find 10% first — just move the decimal point one place — then build from there. 20% off is twice 10%; 15% is 10% plus half of 10%. For a 20% tip, double the 10% figure. The calculator is faster, but the 10%-first trick means you are never helpless without it. The calculator is faster and exact, but the 10%-first trick means you are never helpless without it.
Why do I sometimes see 22.49999999% on calculators?
That is floating-point dust, not a wrong answer. Computers store fractional numbers in binary, and some perfectly ordinary decimals — like 0.1 — cannot be represented exactly, leaving a microscopic residue after arithmetic. Most calculators show you the raw residue; this tool rounds results to a sensible precision first, so you see the clean 22.5% you expected. The underlying value was correct either way.
Are my numbers sent anywhere?
No. Every percentage you compute is calculated locally in your browser by the page's own script. There is no server involved, no account to identify you, and no log of the figures you type. The numbers exist only in the page's memory while you use it and disappear entirely when you leave or refresh. The numbers exist only in the page's memory while you use it and disappear entirely when you leave.
Conclusion
Percentages are simple arithmetic wearing a confusing costume. Pick the shape of your question — a slice, a share, or a change — let the live answer do the rest, and remember the one rule that matters more than any formula: the base always matters more than the rate.