Percentage increase formula

The formula, step by step

1. Subtract the old value from the new value. This is the change, and it can be negative.
2. Divide the change by the old value (use its absolute value if it is negative).
3. Multiply by 100 to turn the decimal into a percentage.

Example: a rent goes from $1,200 to $1,320 a month. The change is $120; $120 ÷ $1,200 = 0.1; × 100 = +10%. If the rent then falls back to $1,200, the change is −$120 ÷ $1,320 = -9.09% — a smaller percentage, because this time the starting point is higher.

Why we divide by the old value

A percentage change answers the question "how big is the change compared with where we started?". The starting point is the reference, so it goes in the denominator. That is why a rise and the fall that undoes it are never the same percentage: a 50% fall needs a 100% rise to recover, and a 20% fall needs a 25% rise.

Percentage change table

The table shows the percentage change from an old value of 80 to a range of new values. The same tool works for any pair of numbers.

Percentage points vs percent

When the values are themselves percentages — interest rates, unemployment, a vote share — be precise. If a mortgage rate goes from 4% to 5%, it rose by 1 percentage point, and that is a 25% increase in the rate. Both statements are true; they measure different things. News reports that say "the rate rose 1%" usually mean one percentage point.

Reversing a percentage change

If you know the value after a change and the size of the change, divide by (1 + change ÷ 100). After a 20% increase a price is $120: the original was 120 ÷ 1.2 = $100.00. After a 15% decrease a price is $85: the original was 85 ÷ 0.85 = $100.00. Simply subtracting or adding the percentage gives the wrong answer ($96.00 and $97.75).

Several changes in a row

Percentage changes multiply; they do not add. A price that rises 10% and then another 10% has risen 21% in total, not 20%. A rise of 10% followed by a fall of 10% leaves you -1% lower than you started. This is the same reason stacked discounts are smaller than they look.

To find the average yearly change over several years (the compound annual growth rate), take the total growth factor to the power of 1 ÷ years and subtract 1. A value that doubles in 10 years grew about 7.18% a year, not 10%.

Percentage difference: when there is no "old" value

Sometimes neither number comes first — two prices in two shops, two measurements of the same thing. Then use the percentage difference, which divides by the average: |a − b| ÷ ((a + b) ÷ 2) × 100. Shop A sells at $10 and shop B at $15: the difference is 40%, the same whichever shop you name first. Percent change would give +50% or -33.33% depending on the order.

Common questions people get wrong

• "Sales went from 0 to 50, what is the increase?" — there is no percentage answer, because you cannot divide by zero; say "from 0 to 50" instead.
• "From −50 to −25 is a decrease, right?" — it is an increase of 50%: the value moved up. Dividing by the absolute old value keeps the sign meaningful.
• "My salary rose 3% and prices rose 5%, so I lost 2%" — roughly. Exactly, your buying power changed by -1.9%.

For quick checks, the percentage calculator answers "what is P% of a number" and "A is what percent of B", which are the building blocks of every change calculation.

Worked examples from everyday life

• Pay rise: a salary going from $52,000 to $54,600 is a raise of 5%. If prices rose 4% over the same year, the real gain is about 0.96%.
• Price drop: a laptop that falls from $1,250 to $999 is -20.08% cheaper — useful when a shop says "save 20%" and you want to check it.
• Website traffic: 18,400 visits in March and 23,000 in April is growth of 25%. Month-to-month figures swing a lot, so compare the same month across years too.
• Fitness: going from 82 kg to 78 kg is a change of -4.88%; a 5 km time falling from 30:00 to 27:00 (1,800 to 1,620 seconds) is -10%.
• Test scores: from 62 to 74 points is +19.35%, but only 12 more points — say which one you mean when you report progress.

How to show percentage change clearly

When you report a change, always give the starting value and the direction, and round to a sensible number of decimals: "+12.5% (from 80 to 90)" is clearer than "12.5%". For values that are themselves percentages, write "percentage points" for the plain difference. In charts, a bar chart of the two values often says more than the percentage alone, because readers can see whether a big percentage comes from a tiny base.

Finally, be careful with averages of percentages. If one product grew 10% and another 50%, the combined growth is not 30% unless both started at the same size; add up the old and new totals first and then compute one change.

Percentage change in spreadsheets

In Excel or Google Sheets, put the old value in A2 and the new value in B2, then type =(B2-A2)/ABS(A2) and format the cell as a percentage. Copy the formula down a column to get the change for every row. Wrap it in IFERROR(…, "") so rows with a zero starting value stay blank instead of showing an error.

Summary

Divide the change by the starting value, multiply by 100 and keep the sign. Reverse a change by dividing, not subtracting. Chain changes by multiplying their factors. Use percentage points for differences between percentages, and the percentage difference when neither value comes first. With those five rules, every percent-change question in news, finance, school or work becomes a two-line calculation that the tool above checks for you.