Percentage Calculator
Work out percentages of a number, percentage change, increase, decrease and reverse percentages, with the working.
30
Working
Answers the seven questions people ask about percentages: a percentage of a number, one number as a percentage of another, the whole from a part, the change between two values, a value after an increase or decrease, the original value before one, and the difference between two values. The answer updates as you type, and the working is shown with your own numbers.
How to use it
Pick a question under Calculate and fill in its sentence. It opens on 15% of 200, which is 30.
- Percentage of a number — a share of a number: a tip, a tax, a discount.
- One number as a percentage of another — also shown as a fraction in lowest terms, which is how marks are usually read.
- The whole, from a part and its percentage — the whole, from a part and the percentage it makes up.
- Percentage change between two values — given as an increase or a decrease, with the multiplier and the change in the opposite direction.
- Increase or decrease by a percentage — the new value, with the amount added or removed.
- Original value before a percentage change — the value before an increase or a decrease, from the value after it: a price before a discount, or before tax was added.
- Percentage difference between two values — for two values where neither is the starting point.
A field takes a number as you would write it: digit grouping (1,234 or 12,34,567), a minus sign, an exponent (1e6), or a fraction (3/4, 1 1/2). A percentage field also accepts a trailing percent sign. Numbers can have up to 100 digits.
Decimal places is Auto, which shows up to 10 significant figures, or a fixed 0 to 6. It applies to the result shown; the working is never rounded to it. On a narrow screen the working sits behind Show working. Everything runs in your browser.
The formulas
Each typed number is read as an exact fraction and the answer is worked out exactly, then rounded once for display, half away from zero. So 10.05% of 10 is 1.005, and at two decimal places it shows 1.01, where floating-point arithmetic holds 1.00499… and would show 1.00. When the digits shown are a rounding, the tool writes ≈ or “about” instead of “is”.
Percentage change divides by the size of the starting value, so a rise from a negative value still reads as an increase: −50 to −25 is an increase of 50%. A change from 0 has no answer (“Percentage change from 0 is undefined.”). Percentage difference divides by the average of the two sizes, so it is the same whichever value comes first and is never negative.
X% of Y = X ÷ 100 × Y
X as a percentage of Y = X ÷ Y × 100
Whole, when X is P% of it = X ÷ P × 100
Percentage change from A to B = (B − A) ÷ |A| × 100
Y increased by P% = Y + Y × P ÷ 100; decreased: Y − Y × P ÷ 100
Original before a P% increase to B = B ÷ (1 + P ÷ 100); before a decrease: B ÷ (1 − P ÷ 100)
Percentage difference of A and B = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
Examples
Marks as a percentage
With One number as a percentage of another, 432 marks out of 500: 432 is 86.4% of 500. As a fraction: 432 of 500 = 108/125 = 86.4%.
- Divide the first number by the second. 432 ÷ 500 = 0.864
- Multiply by 100 to turn it into a percentage. 0.864 × 100 = 86.4%
The price before a 20% discount
With Original value before a percentage change set to decrease, a price of 800 after 20% off: the original was 1,000. Adding 20% back to 800 gives only 960, because the discount was taken from the larger original.
- A decrease of 20% multiplies the original by 1 − 20 ÷ 100. 1 − 0.2 = 0.8
- Divide the final value by that multiplier. 800 ÷ 0.8 = 1,000
A salary rise
With Percentage change between two values: 50,000 to 56,000 is an increase of 12%. Going back, 56,000 to 50,000 is a decrease of about 10.71428571%.
- Subtract the starting value from the new value. 56,000 − 50,000 = 6,000
- Divide by the starting value. 6,000 ÷ 50,000 = 0.12
- Multiply by 100 to turn it into a percentage. 0.12 × 100 = 12%
Change or difference: 40 and 60
Percentage change between two values depends on the direction: 40 to 60 is an increase of 50%, but 60 to 40 is a decrease of about 33.33333333%. Percentage difference between two values has no direction: 40 and 60 differ by 40%. Use change when one value came first, and difference when comparing two things side by side.
Common fractions as percentages
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.3333333333 | 33.33333333% |
| 3/8 | 0.375 | 37.5% |
| 1/2 | 0.5 | 50% |
| 5/8 | 0.625 | 62.5% |
| 2/3 | 0.6666666667 | 66.66666667% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
Frequently asked questions
See also
- Ratio Calculator — to split an amount in a ratio.
- Decimal to Fraction Converter — to write a decimal as a fraction.
- Scientific Calculator — for longer calculations with powers, roots and logs.
- CAGR Calculator — for the yearly growth rate behind a change over several years.