Percentage Calculator

Most percentage mistakes are not arithmetic errors — they come from answering the wrong question. “What is 15% of 200?” and “30 is what percent of 200?” use the same three numbers in different slots, and “prices rose 2 percentage points” means something quite different from “prices rose 2 percent.” This calculator splits the five questions people actually ask into five tabs, so you pick the question first and the formula follows.

The five modes, and the formula behind each

Every tab recalculates as you type, and each one uses a specific formula:

• % of Number — finds a part of a whole: (percent ÷ 100) × number. Use it for a 15% commission on a 200 sale.
• What % is X of Y — turns two raw figures into a share: (X ÷ Y) × 100. Use it for “we sold 30 of the 200 tickets.”
• % Increase — adds a markup on top: N + (N × p ÷ 100). A 150 base plus 20% gives 180.
• % Decrease — takes a cut off: N − (N × p ÷ 100). A 150 base minus 20% gives 120.
• % Change — compares a before and an after: ((To − From) ÷ |From|) × 100. The result is signed, so 100 to 150 shows as +50% and 150 to 100 shows as −33.33%.

The last three are not interchangeable: Increase and Decrease turn a base and a rate into a new amount, while Change turns two amounts into a rate.

Percentage change, percentage difference, and percentage points

These three phrases get used as if they mean the same thing. They do not.

• Percentage change is directional. It measures movement from a starting value, so the starting value sits in the denominator. That is the % Change tab.
• Percentage difference is symmetric — neither value is “first.” It divides the gap by the average of the two: |a − b| ÷ ((a + b) ÷ 2) × 100. There is no tab for it; work out the gap and the average yourself, then use What % is X of Y.
• Percentage points are the plain subtraction of two figures that are already percentages. If a rate moves from 5% to 7%, that is a rise of 2 percentage points — but a 40% relative increase, because 2 is 40% of 5. Both numbers are correct, and quoting the wrong one is one of the easiest ways to mislead a reader.

A quick rule: if both inputs are already percentages, subtract them and say “points.” If they are counts or amounts, use % Change and say “percent.”

Why a 20% drop and a 20% rise do not cancel out

Percentages always attach to a base, and the base moves. Take 100, cut it by 20% and you get 80. Add 20% back to that 80 and you get 96, not 100 — the second 20% was calculated on a smaller number. To undo a 20% decrease you need a 25% increase. For the same reason, two successive 10% discounts are not 20% off but 19% off, because the second applies to the already-reduced price.

The trap also appears when stripping a markup out of a total: if a price already includes a 20% addition, you recover the original by dividing by 1.20, not by subtracting 20%. The discount calculator and the sales tax calculator do that reverse step directly.

Rounding, negatives and empty fields

• Rounding differs per tab. % of Number, % Increase and % Decrease show up to four decimal places; What % is X of Y and % Change show two. Trailing zeros are dropped, so a clean result reads as 30, not 30.0000. The rounding is display-only, so nothing accumulates internally — but a rounded figure copied into a further calculation can drift by a few cents on large amounts.
• Empty boxes count as zero, with one exception: in What % is X of Y, an empty or zero “of” value is treated as 1 to avoid dividing by zero. That gives a very large percentage rather than an error, so check the field is actually filled.
• % Change needs a non-zero starting value. There is no meaningful percentage change from zero, so the tool shows a dash instead.
• Negative bases are handled by magnitude. % Change divides by the absolute value of the starting figure, so a move from −50 to −25 reads as +50% — an improvement — rather than flipping sign.

How to use the Percentage Calculator

1. Pick the tab that matches your question: % of Number, What % is X of Y, % Increase, % Decrease or % Change.
2. Type your figures into the two boxes. Both accept decimals and negative values.
3. Read the large figure in the result panel — it updates on every keystroke, with no button to press.
4. Check the small line underneath, which restates the calculation in words so you can confirm the numbers landed in the slots you intended.
5. Switch tabs to re-frame the same numbers. Each tab keeps its own inputs.

Frequently Asked Questions

Which tab do I use to work out a discount?

Use % Decrease: enter the original price, then the discount rate, and the result is what you pay. For the amount saved instead, use % of Number with the same figures.

How do I find the original price before a discount or a tax?

Not from this tool in one step. Reversing a percentage means dividing rather than subtracting — divide by 1.20 to strip a 20% addition, or by 0.80 to reverse a 20% reduction.

Why does % Change give a different answer if I swap the two numbers?

Because the starting value is the denominator. 100 to 150 is +50%; 150 to 100 is −33.33%. The gap is 50 either way, but it is measured against a different base. That is expected, not a bug.

Can I enter a percentage over 100?

Yes, in every tab. 250% of 40 is 100, and a 150% increase on 200 gives 500. Only the decrease tab produces something odd — rates above 100% push the result below zero, which is correct arithmetic but usually means you wanted a different tab.

Does it handle percentages of percentages?

Yes, but be careful what you call the answer. 10% of 40% is 4% in absolute terms — a change of 4 percentage points, not 4 percent. Enter 10 and 40 in the % of Number tab and label the result yourself.

Why does my result show four decimals?

Three tabs keep up to four decimal places because small percentages of large amounts can otherwise round away entirely. For money, round to two decimals at the end — not partway through a chain of calculations.

Is anything sent to a server?

No. All five formulas run in your browser as you type, and nothing is kept after you close the tab — so note down anything you need before you leave.