Percentage Increase Calculator

This percentage increase calculator gives you the percent change from one number to another as you type. It also does the three jobs people usually need next: add a percentage to a number, work back to the original before an increase, and take a whole list of numbers, a column from a spreadsheet, and show the change at every step with the real average rate.

About the Percentage Increase Calculator

The formula is one line. Where people go wrong is everything around it: going back down, finding the original price, averaging several years of growth, or mixing up percent with percentage points. The Percentage Increase Calculator handles each one and shows its working.

• From one number to another. The percent increase or decrease, the difference, the multiplier, and the percentage it takes to get back.
• Add or remove a percentage. 80 plus 20% is 96. Use a minus sign for a decrease.
• Find the original. What a number was before a percentage increase, by division, the way it has to be done.
• A whole list. Paste up to 1,000 values and get every step, the total change, the biggest rise and fall, and the average rate per step.
• Percentage points. When both numbers are percentages, the difference in points as well.

The Percentage Increase Calculator runs in your browser. Nothing you type or paste is sent anywhere or stored.

How to use the Percentage Increase Calculator

1. Choose what you want to work out from the first menu.
2. Enter your numbers. Commas, dollar signs and percent signs are fine. In list mode, paste a column or separate the values with spaces.
3. Read the result. It updates as you type.
4. Open “Show the working” to see the formula with your numbers in it, then copy or export the result.

The percentage increase formula

Percentage increase = (new value – original value) ÷ original value × 100

A worked example. Your rent goes from $1,200 to $1,350.

1. Difference. $1,350 – $1,200 = $150.
2. Divide by the original. $150 ÷ $1,200 = 0.125.
3. Times 100. 0.125 × 100 = 12.5%.

If the answer comes out negative, it’s a decrease. From $1,500 to $1,200 is (1,200 – 1,500) ÷ 1,500 × 100 = -20%, a 20% decrease. The Percentage Increase Calculator labels it either way.

More examples

Why going back is a different percentage

A 20% cut followed by a 20% rise doesn’t get you back where you started. Take a $1,500 price cut to $1,200. To return to $1,500 it has to rise by $300, and $300 is 25% of $1,200, not 20%. The base you divide by is different each way.

The same thing happens with gains. 50 to 75 is a 50% increase, but 75 back to 50 is only a 33.33% decrease. The Percentage Increase Calculator shows the return figure in its own box so you don’t have to work it out.

Finding the original number before an increase

You know the price after an 8% increase is $86.40. What was it before? The tempting answer is to take 8% off $86.40, which gives $79.49. That’s wrong, because the 8% was a percentage of the original price, not of $86.40.

Divide instead: $86.40 ÷ 1.08 = $80. Check it: $80 plus 8% is $86.40. The same goes for working out a price before sales tax, a salary before a raise, or a population before growth. In the Percentage Increase Calculator, choose “The original number, before a percentage increase”. If you’re taking sales tax out of a receipt, our reverse sales tax calculator is built for exactly that.

Percentage change across a list

This is the mode we built the Percentage Increase Calculator around. Paste the monthly sales, the price of something over the years, or a column of readings, and it does every step at once. Say your rent over four years was:

From first to last that’s a 26.67% increase. The average rate per step is 8.2%. The plain mean of the three step changes is 8.63%, and that’s the number most people quote. It’s the wrong one.

The average percentage increase: why the mean is wrong

Percentage changes multiply, they don’t add. Averaging them as if they add overstates growth whenever the steps vary, and the more they vary, the bigger the error.

The extreme case makes it obvious. A value goes from 100 to 150 (+50%) and back down to 75 (-50%). The mean of +50% and -50% is 0%, yet you’ve lost a quarter of what you started with. The rate that, applied at both steps, takes 100 to 75 is -13.4%:

Average rate per step = (last ÷ first)^{1 ÷ steps} – 1

For the rent example: (1,520 ÷ 1,200)^1/3 – 1 = 8.2%. Apply 8.2% three times to $1,200 and you get $1,520. Apply 8.63% three times and you overshoot. In finance this is called the compound annual growth rate, or CAGR, when the steps are years. The Percentage Increase Calculator shows it whenever the first and last values are above zero, and it shows the plain mean next to it so you can see the difference.

When every step is the same, the two agree. 100, 110, 121, 133.1, 146.41 is 10% a step four times: a 46.41% total, and both averages are 10%.

Percent or percentage points?

When the numbers you’re comparing are themselves percentages, there are two honest answers. A mortgage rate that goes from 3.5% to 4.25% has risen by 0.75 percentage points. As a percentage increase, it’s 21.43%. News reports often say “rose 0.75%”, which is neither.

Tick “Both values are percentages” and the Percentage Increase Calculator gives both. Use points when you’re describing the change in the rate itself. Use the percentage increase when you’re describing how much bigger it got relative to where it was.

Adding a percentage to a number

To add 4% to $60,000, multiply by 1.04: $62,400. To take 15% off, multiply by 0.85. The multiplier is 1 plus the percentage as a decimal, and it works for decreases if the percentage is negative. In the Percentage Increase Calculator, pick “A number increased (or decreased) by a percentage” and type -15 for a 15% decrease.

Zero, negative numbers and big jumps

• From zero. The percentage increase from 0 is undefined, because the formula divides by the original value. Going from 0 to 12 sales is a gain of 12, but not any percentage of nothing. The calculator says so and gives the difference.
• To zero. Any positive number falling to 0 is a 100% decrease. Nothing can fall by more than 100%.
• Negative starting values. The change is divided by the size of the original, so -50 to -25 is a 50% increase: the number went up. The page tells you when this applies. Some textbooks leave percentage change undefined for negative bases, so check what your course expects.
• Over 100%. An increase can be any size. From 1 to 3 is +200%: the new value is three times the old, which is 200% more.

Percentage increase or percentage difference?

They answer different questions. A percentage increase has a direction: it starts from the original and asks how far the new value moved. A percentage difference has no starting point. It compares two values as equals, dividing the gap by their average:

Percentage difference = |a – b| ÷ ((a + b) ÷ 2) × 100

For 50 and 75 that’s 25 ÷ 62.5 × 100 = 40%, whichever way round you put them. Use the percentage increase for anything that changed over time: a price, a salary, a score. Use the percentage difference when neither value came first, such as two shops’ prices for the same item or two lab readings.

The same formula in a spreadsheet

With the original in A2 and the new value in B2, the percentage increase is =(B2-A2)/A2, formatted as a percentage. Fill it down and you get every step. The average rate per step across a column from A2 to A10 is =(A10/A2)^(1/8)-1, where 8 is the number of steps, one fewer than the number of values. Getting that count wrong by one is a very common slip. The list mode in the Percentage Increase Calculator counts the steps for you: paste the column straight from the spreadsheet and it reads one value per line.

Where the percentage increase comes up

• A pay rise. $60,000 to $66,000 is a 10% raise. Compare it with inflation over the same year to see whether you’re ahead.
• Rent and bills. Check a renewal notice. A $1,200 rent going to $1,350 is 12.5%, which some cities cap by law.
• Prices. A sale price, a shrinking pack size, or what a subscription now costs compared with last year.
• Business figures. Month-on-month revenue, sign-ups or traffic. List mode gives every month and the average growth rate at once.
• Schoolwork. Percentage change questions, with the working laid out in the order a teacher expects.

Common mistakes

• Dividing by the new value. Always divide by the original, the number you started from.
• Subtracting to undo an increase. Divide by 1 plus the rate instead.
• Averaging percentage changes. Use the average rate per step from list mode.
• Calling a points change a percent change. 3.5% to 4.25% is 0.75 points and 21.43%.
• Expecting -20% then +20% to cancel. It leaves you 4% down.

How the Percentage Increase Calculator works

1. Change: (new – original) ÷ |original| × 100. Undefined when the original is 0.
2. Apply: value × (1 + percentage ÷ 100).
3. Original: value ÷ (1 + percentage ÷ 100). Undefined for a 100% decrease.
4. List: the change formula at every step; the total from first to last; the average rate (last ÷ first)^1/steps – 1; and the plain mean of the steps.
5. Rounding is for display only: 2 decimal places, or 4 significant figures for very small changes. The working is done at full precision.

Working out what a rate change does to a loan? The home loan calculator shows the payment and total interest for any rate. To see what steady percentage growth adds up to with reinvested dividends, try the DRIP calculator.