Percentage change vs percentage points: calculate the right difference
Compare price changes, rates and growth correctly, with worked examples, reverse calculations and common percentage mistakes.
Start with the number you are comparing
A price, a salary and an interest rate can all change, but the correct description depends on the starting quantity. For ordinary values, percentage change = (new − old) ÷ old × 100. Always divide by the original value, not the final one. Keep currency, period and measurement basis consistent.
A price rising from 80 to 100 increases by 20 ÷ 80 × 100 = 25%. Enter both values in the percentage change calculator. The original value must be nonzero; growth from zero has no finite percentage change under this formula.
When both numbers are percentages
If a conversion rate rises from 4% to 5%, the difference is 1 percentage point. Relative to the old rate, the increase is (5 − 4) ÷ 4 × 100 = 25%. Both statements are correct, but they describe different comparisons. The ONS explanation of percentage points distinguishes these terms.
Why a fall and recovery are not symmetric
A 20% fall takes 100 to 80. Recovering from 80 to 100 needs a 25% increase because the denominator is now smaller. Similarly, two successive 10% discounts give 100 × 0.9 × 0.9 = 81, a total reduction of 19%, not 20%. Use the discount calculator for one reduction and compare the final price with the original.
Reverse a percentage increase
If the final price after a 15% increase is 230, divide by 1.15 to recover 200. Subtracting 15% from 230 gives a different answer. For several years, the CAGR calculator gives an equivalent compound annual rate; it does not show each year’s actual change. Read compound interest with monthly contributions before comparing growth that includes deposits.
Quick checks before reporting a result
Is the baseline zero or negative? Negative baselines need extra interpretation; show the raw change as well. Are you comparing equal time periods? Have you distinguished a rate difference from relative growth? Report the original and new values alongside the percentage so readers can reproduce it.