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CALCULATOR · Math

Percentage Calculator

Three percentage questions in one tool: P% of X, X is what % of Y, X is P% of what.

Show formula
P%·X = P·X/100 · X/Y × 100 · X ÷ (P/100)

Inputs

Enter a percentage and a number to find the result.

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Result

Your result appears here

Enter Percentage (%) / Base value (X) and the result fills in as you type.

How it works

  1. Pick one of the three percentage questions.
  2. Fill in the two known values.
  3. Read the answer — the applied formula is shown underneath.

Frequently asked questions

What are the three modes?

"P% · X" finds a percentage of a value, "X / Y" asks what percent one value is of another, and "X = P% · ?" finds the whole when you know a part and its percent.

Why can some inputs fail?

Division by zero has no answer, so a zero base or zero percentage returns a clear error instead of a wrong number.

What is the formula for a percentage?

Percentage = part ÷ whole × 100. The other two forms are the same formula rearranged: part = whole × percentage ÷ 100, and whole = part ÷ percentage × 100.

How do I work out a percentage increase?

Subtract the old value from the new one, divide by the old value and multiply by 100: from 50 to 65 is 15 ÷ 50 × 100 = 30%. The Percentage Change Calculator does this in one step and handles decreases too.

Why don’t a 10% rise and a 10% fall cancel out?

Because the second percentage is taken of a different number. 10% of 100 is 10, giving 110, but 10% of 110 is 11, giving 99. As multipliers: 1.10 × 0.90 = 0.99.

How do I work out 15% without a calculator?

Find 10% by moving the decimal point one place to the left, then add half of it: for 240, 10% is 24, half of that is 12, and 24 + 12 = 36.

One relation, three questions

Every percentage question is the same sentence with one number missing: P% of X is Y. The calculator’s three modes solve that sentence for each of the three blanks.

  • The part, Y. Y = X × P ÷ 100. 15% of 240 is 240 × 15 ÷ 100 = 36.
  • The percentage, P. P = Y ÷ X × 100. 36 out of 240 is 36 ÷ 240 × 100 = 15%.
  • The whole, X. X = Y ÷ P × 100. If 36 is 15% of a number, the number is 36 ÷ 15 × 100 = 240.

The three examples share the same three numbers because they are one multiplication, rearranged. Percent means per hundred, so 15% is simply 0.15, and taking 15% of something is the same as multiplying it by 0.15.

Common percentages at a glance

The percentages people use most, the fraction each one stands for, a mental shortcut, and the result on 240:

Common percentages of 240
PercentOf 240FractionShortcut
1%2.41/100move the decimal point two places to the left
5%121/20half of 10%
10%241/10move the decimal point one place to the left
12.5%301/8halve three times
15%363/2010% plus half of that
20%481/5divide by 5
25%601/4halve twice
33⅓%801/3divide by 3
50%1201/2halve
66⅔%1602/3a third, doubled
75%1803/4a half plus a quarter
100%2401/1the number itself

The 10% row does most of the everyday work: halve it for 5%, double it for 20%.

Mistakes that change the answer

  • Percentage points versus percent. A rate that rises from 3% to 3.5% has gone up by 0.5 percentage points, which is a 16.7% increase. Reporting one as the other misstates the change more than thirtyfold.
  • Dividing by the wrong number. A price that goes from 240 to 300 has risen by 60 ÷ 240 = 25%. Dividing by the new price instead gives 20%, which answers a different question.
  • Undoing a change with the same percentage. A price cut by 20%, from 50 to 40, needs a 25% rise to get back to 50, not a 20% one.
  • Removing tax by subtracting its rate. 100 plus 20% tax is 120, but 120 minus 20% is 96. The price before tax is 120 ÷ 1.2 = 100.
  • Adding up discounts. 20% off followed by another 10% off is not 30% off: 100 becomes 80, then 72, a total discount of 28%.
  • Typing a decimal into a percent field. 0.15 in a field that expects a percentage means 0.15%, not 15%, and the answer comes out 100 times too small.
  • Distrusting answers over 100%. 250% of 20 is 50. A percentage above 100 simply means the part is larger than the number it is compared with, as when a price more than doubles.

Examples

What is 20% of 150?
30. Use the first mode with P = 20 and X = 150.
18 is what percent of 60?
30%. The second mode divides the part by the total.
12 is 40% of what number?
30. The third mode recovers the whole from a part and its share.

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