Percentage Calculator

How to use it

1. Pick the question, then fill in the two numbers. The labels change with the question, because "15% of 200" and "15 is what percentage of 200" take the same two numbers in a different order — mixing them up is the most common way to get a plausible wrong answer.
2. Do not add a percent sign. Type 15 for 15%. A trailing % is accepted, but a bare number is simpler. Thousands separators and negative signs are both handled.
3. Read the formula row. Every result comes with the arithmetic that produced it, so you can check it against the numbers you actually entered rather than trusting the output.

The four formulas

Every question on this page is one of four rearrangements of the same relationship. Naming the question is most of the work; the arithmetic is trivial once you have:

The vertical bars mean "absolute value" — the size of the number without its sign. Why that matters is the part most calculators skip, so there is a section on it below.

Percentage change is not percentage difference

These two are routinely confused, and the confusion produces numbers that are wrong in a subtle way.

• Percentage change has a direction and a base. From 100 to 120 is +20%. From 120 back to 100 is −16.7%, not −20%, because the base is now 120. That asymmetry is not a trick: it is why a 20% fall does not undo a 20% rise, and why investments that drop 50% need a 100% gain to recover.
• Percentage difference compares two values with neither treated as the starting point. It uses their average as the base: 100 and 120 differ by 20 ÷ 110 × 100 ≈ 18.2%. Use it when you have two measurements of the same quantity — two readings, two estimates, two reviewers' scores.

This page handles percentage change, because that is what the question "from X to Y" means. If you want percentage difference, calculate the average of the two values first, then use the change mode with the average as the starting value — the arithmetic is the same, and doing it explicitly keeps you honest about which base you chose.

Percentage points are not percentages

A rate rising from 4% to 6% has risen by 2 percentage points and by 50%. Both numbers describe the same change, and quoting the wrong one changes the story entirely.

The difference is what you are measuring against. The 2 is a subtraction between two rates. The 50% is the relative size of the move, and you get it from the percentage change formula:

(6 − 4) ÷ 4 × 100 = 50%

So when you read that something "increased by 2%", check which of the two is meant. In reporting about interest rates, unemployment, test pass rates and conversion rates, the distinction matters more than the arithmetic: a climb from 4% to 6% sounds small as two points and large as fifty per cent.

You cannot take a percentage of zero

Dividing by zero has no answer, and percentages hide that fact rather than showing it. Two cases come up:

• What percentage is 5 of 0? Undefined. It is tempting to answer 0%, but 0% would mean "5 is nothing of 0", which is not a meaningful statement.
• What is the percentage change from 0 to 5? Also undefined. As a proportion of the original value, every increase from zero is infinitely large, and no single number describes it.

Rather than print 0% or Infinity, both of which look like results, this calculator says the quantity is undefined and explains why. When a base is genuinely zero, quote the absolute change — "up 5, from nothing" — because that is true and useful where a percentage is not.

Negative numbers: what increase and decrease mean here

Percentages of negative numbers are where calculators start disagreeing with each other, so this page states its rule instead of leaving you to discover it.

Both the change mode and the increase/decrease modes measure the percentage against the size of the starting value — its absolute value. The consequence is that the sign always tells you which way the number moved:

Where this differs from a spreadsheet. Excel and Google Sheets define a 10% increase as multiplying by 1.1, so they return −110 for a 10% increase of −100. That convention makes "increase" produce a smaller number, which is defensible arithmetic and confusing language. Here, "increase" always moves the number up and the change mode always agrees with it: −100 increased by 10% is −90, and the change from −100 to −90 is +10%. The two modes are consistent with each other, which matters more when you use both on one page.

For positive numbers the two conventions are identical, so this only affects you if you are working with losses, debts, temperatures or other values below zero. If a figure must match a spreadsheet, use the spreadsheet.

Checking a percentage without a calculator

Percentages are easy to sanity-check in your head, which is worth doing because a decimal-point slip is the most common error:

• 10% is a decimal shift. 10% of 200 is 20, 10% of 4,500 is 450. Start there and build up.
• 5% is half of 10%. So 15% of 200 is 20 + 10 = 30 — two steps, no calculator.
• 1% is two decimal shifts. 1% of 250 is 2.5, so 3% is 7.5.
• A percentage change should be plausible in size. If a value went from 100 to 150 and you get 5%, something is off by a factor of ten; if it went from 100 to 105 and you get 50%, the base is wrong.

Rounding is the other place answers drift. This calculator shows up to four decimal places and does not round intermediate steps, so 1 ÷ 3 stays 0.3333 through the calculation rather than becoming 0.33 and losing accuracy. If you are comparing two results, round both at the end, not in the middle.

Where to go next

• Word and character counter — the other side of text work: words, characters, sentences and reading time.
• Job offer comparison calculator — percentages applied to the thing people most often want to compare.
• Everyday tools — the rest of this category: dates, working days and text counts.

Common questions

How do I calculate a percentage increase?

Subtract the original from the new value, divide by the original, and multiply by 100. From 100 to 150 the difference is 50, divided by 100 gives 0.5, so the increase is 50%. Equivalently, 150 ÷ 100 = 1.5, which is 1 plus 0.5 — the 0.5 is the increase. The calculator uses the absolute value of the original as the divisor, so with negative starting values the sign still tells you the direction of movement.

What is the difference between percentage change and percentage difference?

Percentage change has a direction and uses the original value as its base: from 100 to 120 is a 20% increase, and from 120 back to 100 is a 16.7% decrease — not 20%, because the base moved. Percentage difference compares two values without either being the starting point, using their average as the base: 100 and 120 differ by about 18.2%, because 20 ÷ 110 = 0.182. Use change when one value came first, and difference when you have two measurements of the same thing.

Is a rise from 4% to 6% a 2% increase?

It is a rise of 2 percentage points, and a 50% increase. Both statements are correct and mean different things, which is why rates are so often misread. The 2 is the arithmetic difference between the two rates; the 50% is how much larger 6% is than 4%. Politicians, journalists and reviewers slip between the two constantly, sometimes without meaning to. When someone quotes a change in a rate, work out which one they mean before you repeat it.

Why can you not calculate a percentage change from zero?

Because every rise from zero is infinitely large as a proportion of the original. Going from 0 to 5 is not a 500% increase — the question has no answer, since dividing by zero is undefined. Falling from 0 to a negative number is a different situation again, and also has no percentage. This calculator says so rather than printing 0% or infinity, both of which look like answers. If a base is genuinely zero, quote the absolute change instead.

How do I work out the original price before a discount?

Divide the price you paid by the percentage it represents. If 75% of the original price is 60, the original is 60 ÷ 0.75 = 80. That is the same relationship as "what percentage is X of Y", rearranged: X = Y × p ÷ 100, so Y = X × 100 ÷ p. The reverse percentage is deliberately not a separate button, because it is the same formula — and knowing which rearrangement you need is the part worth understanding.

What does a negative percentage change mean?

It means the value moved in the negative direction: 100 to 80 is −20%. With negative starting values the same rule reads slightly differently, because this calculator measures the change against the size of the starting value. Going from −100 to −50 is reported as +50%, since the number moved upward and the size of the loss halved. The sign is always the direction of movement, never a judgement about whether the change was good.