How to Calculate Percentage Increase (Formula and Examples)

Percentage increase tells you how much a value has grown relative to where it started, expressed as a percentage. It is the maths behind a pay rise, a price hike, a jump in website traffic, or a population that grew over a decade. The calculation is short, but one small slip, dividing by the wrong number, throws the whole answer off. This guide walks through the formula, a clear worked example, a reference table, and the mistakes to avoid.

The percentage increase formula

There is only one formula to remember, and it has three moving parts: the original value (where you started), the new value (where you ended up), and the difference between them.

The reason you divide by the original value is that percentage change always measures growth relative to the starting point. A jump of 10 is huge if you started at 20, but tiny if you started at 2,000. Dividing by the original is what turns a raw difference into a meaningful percentage. This is the same idea covered in our guide to percent change, which handles both increases and decreases in one formula.

A worked example, step by step

Suppose your monthly rent went from 1,200 to 1,380 dollars. Here is how to find the percentage increase.

1. Identify the original value and the new value. Original is 1,200 and new is 1,380.
2. Subtract the original from the new to get the difference. 1,380 minus 1,200 equals 180.
3. Divide the difference by the original value. 180 divided by 1,200 equals 0.15.
4. Multiply by 100 to turn the decimal into a percentage. 0.15 times 100 equals 15.
5. Read the result. The rent increased by 15 percent.

Notice that step 3 divides by 1,200, the original rent, and not by 1,380. If you accidentally divided by the new value you would get about 13 percent, which is wrong. Keeping the original in the denominator is the single most important habit to build.

It helps to verify the answer in reverse. If the rent really rose by 15 percent, then 1,200 times 1.15 should land back on 1,380, and it does. This quick check catches almost every arithmetic slip before it becomes a problem. Whenever your percentage looks suspiciously large or small, run the original value times one plus your percentage and confirm it matches the new value you started with.

What a negative result means

The same formula works whether a value goes up or down. If your answer is negative, the value did not increase, it decreased by that amount. There is no separate formula to learn for a drop.

So a positive answer is an increase and a negative answer is a decrease. If you only ever care about the size of the change and not the direction, you can ignore the sign, but in most real situations the direction matters. For a deeper look at handling both directions cleanly, see our average rate of change explainer.

One subtlety worth knowing: an increase and the matching decrease are not symmetric. If a price rises 25 percent and then falls 25 percent, you do not end up back where you started. Starting at 80, a 25 percent rise gives 100, and a 25 percent fall from 100 gives 75, which is below the original 80. The reason is that each percentage is taken from a different base. This is exactly why you must always pin down which value is the original before you divide, because swapping the base quietly changes the answer.

Quick reference table

These worked examples show the formula in action across a range of starting and ending values. Each row applies the same three steps: difference, divide by original, times 100.

Where you will actually use this

Percentage increase shows up far more often than its short formula suggests. Knowing where it appears makes the maths feel less abstract and helps you spot when someone is presenting a number in a misleading way.

• Salary and pay rises. A raise from 48,000 to 52,800 is a 10 percent increase: 4,800 divided by 48,000, times 100. Quoting the raw 4,800 sounds bigger than the modest percentage it really is.
• Pricing and inflation. A coffee that climbs from 4.00 to 4.60 has risen 15 percent. Tracking these small increases over a year explains how budgets quietly tighten.
• Business and marketing metrics. Traffic going from 10,000 to 12,500 monthly visitors is a 25 percent increase. Growth is almost always reported as a percentage so different sized numbers can be compared fairly.
• Investing and savings. A portfolio rising from 5,000 to 5,400 gained 8 percent. Percentage returns let you compare investments of wildly different sizes on equal footing.
• Everyday comparisons. Recipe scaling, tip estimation, and fuel efficiency changes all lean on the same subtract, divide, multiply pattern.

Common mistakes to avoid

Most percentage increase errors come down to a handful of repeat offenders. Watch for these.

• Dividing by the new value. Always divide by the original (starting) value. Dividing by the new value gives a smaller, incorrect figure.
• Confusing percentage points with percent. Going from 10 percent to 15 percent is a rise of 5 percentage points, but a 50 percent increase in relative terms. They are not the same number.
• Forgetting to multiply by 100. Stopping at the decimal (0.15) and calling it the answer. You must multiply by 100 to express it as a percentage.
• Mixing up which value is original. If you swap the new and original values, the sign and the size of the answer both change. Label them before you start.
• Ignoring a negative sign. A negative result is a real decrease, not a mistake to erase. The sign carries meaning.

Good to know: reversing the calculation

Sometimes you know the original value and the percentage increase, and you want the new value. Multiply the original by one plus the percentage as a decimal. To add 15 percent to 1,200, compute 1,200 times 1.15, which equals 1,380. This shortcut is handy for projecting next year's price or a salary after a raise.

If a value grows by the same percentage repeatedly, the increases compound rather than simply adding up. Two back to back 10 percent rises do not make 20 percent, they make 21 percent, because the second rise applies to the already larger value. That compounding behaviour is the heart of compound interest and of exponential growth more generally.

Calculate it instantly

Once the method clicks, a calculator saves time and removes the risk of dividing by the wrong number. Enter your original and new values below and the tool returns the percentage increase, along with the difference, in one step.

Percentage increase is one of those small skills that pays off everywhere, from reading a salary offer to checking whether a price hike is fair to tracking how fast a number is growing. Remember the one rule that matters most: subtract, then divide by the original value, then multiply by 100. Get that division right and the rest is easy.