Percentage Calculator

This is the general-purpose reference tool for the three percentage questions that come up most: what is X% of Y, what percent one number is of another, and the percentage increase or decrease between two values. Every answer comes with the formula and the working, so it doubles as a way to check your own math. If you have a specific job in mind, our Percent Off Calculator handles shop discounts and our Salary Increase Calculator handles pay rises. This page covers the underlying math those two are built on.

Pick the type of percentage question you need to solve

What is X% of Y?

Percentage (X)

Of value (Y)

Your answer will appear here

Fill in the fields for your chosen question type, then click calculate to see the result and the working.

Quick Answer

To find X% of Y, multiply Y by X ÷ 100. To find what percent X is of Y, divide X by Y and multiply by 100. To find a percentage change, subtract the old value from the new value, divide by the old value, and multiply by 100 — a positive answer is an increase, a negative one is a decrease.

How It Works: Formula & Variables

1. What is X% of Y

Result = (X ÷ 100) × Y

2. X is what percent of Y

Percentage = (X ÷ Y) × 100

3. Percentage change from Y (old) to Z (new)

% change = ((Z − Y) ÷ Y) × 100

Positive is an increase, negative is a decrease. The base is always the old value Y, never the new value.

Need more depth here, such as percent versus percentage points, a negative starting value, or a run of periods side by side? Use our Percentage Change Calculator.

Handy follow-up formulas

Apply an increase: New = Old × (1 + X/100)
Apply a decrease: New = Old × (1 − X/100)
Reverse a change: Original = Final ÷ (1 ± X/100)

The reverse formula is how you recover a starting figure — for instance, the price before a discount was applied.

Worked Examples

Example 1: What is 15% of 200?

Turn the percentage into a decimal first, then multiply. (15 ÷ 100) × 200 = 0.15 × 200 = 30.

Example 2: 45 is what percent of 180?

Divide the part by the whole, then scale to a percentage. (45 ÷ 180) × 100 = 25%.

Example 3a: Percentage increase from 50 to 65

The gap is 15, and the base is the old value of 50. ((65 − 50) ÷ 50) × 100 = 30% increase.

Example 3b: Percentage decrease from 800 to 600

Same formula, and the base is still the old value of 800. ((800 − 600) ÷ 800) × 100 = 25% decrease.

Key Concepts

Percent means "out of 100": A percentage is just a fraction with 100 on the bottom. That is why every calculation either divides by 100 to turn a percent into a decimal, or multiplies by 100 to turn a decimal back into a percent.

The base is what you compare against: "X% of Y" and "percentage change" both hinge on picking the right base. For a change, the base is the starting figure. Measure the same jump against a different base and you get a different percentage.

Percentage points vs. percentage change: These answer different questions. Points are the straight difference between two rates; a percentage change is that difference measured relative to where you started. A move from 40% to 44% is 4 percentage points but a 10% relative increase.

Two of these are reverses of each other: "What is X% of Y" and "X is what percent of Y" run the same numbers in opposite directions. One hands you the amount, the other hands you the rate, so it pays to be sure which one the question wants.

Common Mistakes

Mixing up percentage points and percentage change: Reading 40% to 44% as a 4% change instead of 4 percentage points (a 10% relative increase) throws the answer off badly. Decide which one you actually mean before you calculate.

Using the wrong base on a change: For an increase or decrease, always divide by the old value, not the new one. Dividing by the new figure quietly gives you the wrong percentage.

Rounding too early: Convert to a decimal and do the full multiplication first, then round the final answer. Rounding partway through drags the result off.

Forgetting the ÷100 step: Multiplying by the raw percentage (15) instead of the decimal (0.15) inflates the answer tenfold. The percent has to become a decimal before it multiplies anything.

Confusing the two "of" questions: "What is X% of Y" and "X is what percent of Y" are opposite operations. Running one when you meant the other is an easy way to get a number that looks plausible but is wrong.

Frequently Asked Questions

Subtract the old value from the new value, divide by the old value, then multiply by 100. Going from 50 to 65 is (15 ÷ 50) × 100 = 30%. The old value is always the base you divide by, not the new one.

A percentage point is the plain arithmetic gap between two percentages, so you just subtract them. A percentage change is relative to a starting point, so you divide and then compare. A rate that goes from 3% to 4% rises by 1 percentage point, but by 33% in relative terms. Another way to see it: 40% to 44% is 4 percentage points, but a relative increase of 10%.

Divide by 100, which is the same as moving the decimal point two places to the left. So 50% becomes 0.5, and 67.5% becomes 0.675. Reverse it to go the other way: multiply a decimal by 100 to get a percentage.

Yes. x% of y always equals y% of x. For example, 10% of 15 and 15% of 10 both come out to 1.5. When you are working something out in your head, pick whichever order is easier to multiply.

Divide the final value by (1 ± X/100). Use a minus for a decrease and a plus for an increase. An item that costs $80 after a 20% discount started at 80 ÷ (1 − 0.20) = $100. This is not the same as adding 20% back onto $80, which is a common slip.

Divide the part by the whole and multiply by 100: (X ÷ Y) × 100. For instance, 15 is (15 ÷ 300) × 100 = 5% of 300. This is the reverse of "what is X% of Y", so watch which one the question is actually asking.

Last reviewed 2026-07-24. For educational purposes only — not professional advice.