Percentage Calculator

What is a percentage calculator?

A percentage calculator is a tool that solves the three most common percentage problems: finding a percentage of a number, working out what percent one number is of another, and measuring the percentage change between two values. A percentage is simply a fraction expressed out of 100, so “25%” means 25 per 100, or 0.25.

This calculator handles all three calculations in one place. You pick a mode, enter two numbers (X and Y), and it returns either a plain value or a percentage. Because percentages underpin everything from sales tax and tips to test scores and price changes, knowing which of the three formulas to use is the key skill — the arithmetic itself is easy once the setup is right.

What are the three percentage formulas?

There are three core formulas, and this tool uses each one exactly as written below.

• X% of Y = (X ÷ 100) × Y — here X is the percent, Y is the value
• X is what % of Y = (X ÷ Y) × 100 — here X is the part, Y is the whole
• Percentage change from X to Y = ((Y − X) ÷ |X|) × 100 — here X is the original, Y is the new value

In the change formula, dividing by the absolute value of the original keeps the sign meaningful: a positive answer is an increase, a negative answer is a decrease. The tool shows a leading + for increases so the direction is never ambiguous.

How do you calculate a percentage of a number?

Multiply the value by the percentage divided by 100. This answers questions like “what is the tax?” or “how big is the discount?”

Worked example 1 — 20% of 80. Using (X ÷ 100) × Y with X = 20 and Y = 80: (20 ÷ 100) × 80 = 0.2 × 80 = 16.

Worked example 2 — 15% of 240. (15 ÷ 100) × 240 = 0.15 × 240 = 36. So a 15% service charge on a $240 bill is $36, making the total $276.

How do you find what percent one number is of another?

Divide the part by the whole, then multiply by 100. This turns a raw count into a proportion.

Worked example 1 — 45 is what percent of 180? Using (X ÷ Y) × 100 with X = 45, Y = 180: (45 ÷ 180) × 100 = 0.25 × 100 = 25%.

Worked example 2 — 18 is what percent of 60? (18 ÷ 60) × 100 = 0.3 × 100 = 30%. If you scored 18 out of 60 on a quiz, that is 30%. Note that Y (the whole) cannot be zero, or the result is undefined.

How do you calculate percentage increase and decrease?

Subtract the original from the new value, divide by the original, and multiply by 100. A positive result is an increase; a negative result is a decrease.

Worked example 1 — a price falls from $80 to $60. ((60 − 80) ÷ |80|) × 100 = (−20 ÷ 80) × 100 = −25%, a 25% decrease.

Worked example 2 — revenue rises from 200 to 260. ((260 − 200) ÷ |200|) × 100 = (60 ÷ 200) × 100 = +30%, a 30% increase.

A common trap: a percentage increase and the same-sized percentage decrease do not cancel out, because they are taken from different bases. Drop 100 by 50% to get 50, then raise 50 by 50%, and you reach only 75 — not 100. To compute markups and margins specifically, the markup calculator handles cost-to-price conversions directly.

What is the difference between percentage points and percent?

Percentage points are the plain arithmetic gap between two percentages; percent describes the relative change. They are not interchangeable.

Suppose an interest rate rises from 40% to 45%. The increase is 5 percentage points (45 − 40). But as a percent change, it is (5 ÷ 40) × 100 = 12.5% relative to the starting value. Newspapers often blur this — saying a rate “rose 5%” when it actually rose 5 percentage points — so always check whether a figure is an absolute gap or a relative change.

Starting %	Ending %	Percentage-point change	Percent change (relative)
40%	45%	+5 points	+12.5%
10%	12%	+2 points	+20%
80%	60%	−20 points	−25%
5%	10%	+5 points	+100%
50%	25%	−25 points	−50%

How do you reverse a percentage to find the original amount?

Divide the final amount by 1 plus the percentage as a decimal (for an increase) or 1 minus it (for a decrease). This “undoes” a percentage change.

If an item costs $120 after a 20% increase, the original was 120 ÷ (1 + 0.20) = 120 ÷ 1.20 = $100. If a price is $170 after a 15% discount, the pre-discount price was 170 ÷ (1 − 0.15) = 170 ÷ 0.85 = $200. A frequent mistake is subtracting 20% of $120 instead of dividing — that gives $96, which is wrong, because the 20% was originally taken from the smaller base of $100.

A quick percentage reference chart

This table converts common percentages to decimals and fractions, which speeds up mental math.

Percentage	Decimal	Fraction	Example: of 200
1%	0.01	1/100	2
5%	0.05	1/20	10
10%	0.10	1/10	20
12.5%	0.125	1/8	25
25%	0.25	1/4	50
33.33%	0.3333	1/3	66.67
50%	0.50	1/2	100
75%	0.75	3/4	150
100%	1.00	1/1	200

Tips and common mistakes

• Match the mode to the question. “Of” gives a value; “is what percent” and “change” give a percentage. Mixing them up is the number-one error.
• Watch the base. Percentage change always divides by the original value, not the new one.
• Don’t confuse points and percent (see above) — especially with rates and survey results.
• Avoid double-counting. Applying a 10% discount and then a 5% tax is not a flat 5% change; apply each step in sequence.
• Reverse with division, not subtraction, when recovering a pre-tax or pre-discount price.

Limitations and accuracy notes

This calculator computes in full floating-point precision and then displays results rounded to up to four decimal places, with trailing zeros removed — so percentage-change figures that produce repeating decimals (for example, 1 of 3) are shown as rounded approximations. The tool also requires valid inputs: the whole (Y) cannot be zero when finding “what percent,” and the original (X) cannot be zero for a percentage change, since dividing by zero is undefined.

Percentages describe relationships, not absolute size, so a “200% increase” on a tiny base can still be a small number in real terms — always keep the underlying figures in view. For related calculations, see the Math tools category or compute averages with the mean, median, and mode calculator.