Percentage Calculator

How to use the percentage calculator

1. Find the row that matches your question. The five rows are independent, so you can fill in one, several or all of them.
2. Type your numbers into the boxes. The answer to the right of the equals sign updates with every keystroke; there is no button to press.
3. Clear a box and that row shows a dash instead of an error message.

The page loads with an example in each row so you can see the layout: 20% of 80, 16 as a percentage of 80, the change from 50 to 65, 100 increased by 15%, and 80 decreased by 20%.

What each row calculates

• What is X % of Y: multiplies Y by X and divides by 100. 15% of 200 is 200 x 15 / 100 = 30.
• X is what % of Y: divides X by Y and multiplies by 100. 45 out of 180 is 45 / 180 x 100 = 25%. If Y is 0 or blank the row shows a dash, since the question has no answer.
• Change from A to B: subtracts A from B, divides by the size of A and multiplies by 100. Going from 50 to 65 gives +30%; going from 65 down to 50 gives about -23.08%. A positive result carries a plus sign.
• Increase by: multiplies the value by 1 plus the rate. 100 increased by 15% is 115.
• Decrease by: multiplies the value by 1 minus the rate. 80 decreased by 20% is 64.

Results are rounded to six decimal places and shown with thousands separators, so 1234567 x 5% appears as 61,728.35 rather than a long string of digits. If the starting value in the change row is negative, the tool divides by its absolute value, so the sign of the result still shows whether the number went up or down in the direction you would expect. A start value of 0 gives a dash because the percentage change from zero is undefined.

Worked examples from daily life

• Sale price: a jacket costs 129.90 and is 30% off. Use "Decrease by" with 129.90 and 30 to get 90.93, a saving of 38.97.
• Tip: a 62.50 restaurant bill with an 18% tip. "Increase by" gives 73.75. For just the tip amount, use the first row: 18% of 62.50 is 11.25.
• Exam score: 37 correct out of 45 questions. The second row gives 82.2222%.
• Price comparison: a subscription rises from 9.99 to 11.99. The change row gives +20.02%, which is the figure to compare with a quoted inflation rate.
• Adding VAT or sales tax: increase the net price by the tax rate. To go the other way and find the net price from a gross one, divide by 1 plus the rate, so 110 gross at 10% tax is 100 net. Taking 10% off 110 would give 99, which is wrong.

Common mistakes

• Reversing a percentage change. A 20% cut takes 80 to 64, but putting the 20% back on 64 only reaches 76.8. To undo a 20% decrease you need a 25% increase, because the base changed. Run it through the change row (64 to 80 = +25%) to check.
• Mixing up percent and percentage points. If an interest rate moves from 4% to 5%, it rose by 1 percentage point, but the relative change is +25%. Enter 4 and 5 in the change row to see that figure.
• Stacking percentages by adding them. A 10% rise followed by a 10% fall does not cancel out: 100 becomes 110, then 99. Run the two steps one after another instead of adding or subtracting the rates.
• Using the wrong base. "X is what % of Y" and "Y is what % of X" give different answers. 20 is 25% of 80, but 80 is 400% of 20.

Tips and limits

• Percentages above 100 are fine. Increasing 50 by 200% gives 150, and a change from 10 to 50 is +400%.
• Decreasing by more than 100% produces a negative number, which is mathematically correct but rarely what you meant. Check that you typed the rate in the right box.
• The calculator works with plain numbers. It does not handle currency symbols, commas typed into the boxes or unit conversions.
• Very small or very large inputs are limited by the standard precision of numbers in a browser, which is about 15 significant digits.

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