Percentage Change

What this page measures — and what it doesn't

Every percentage change has three parts: where you started, where you ended, and the direction between them. This calculator gives you the relative change — (new − original) ÷ |original| × 100 — and refuses the classic trap of dividing by the new value, which quietly shrinks every result when the figure grew. Enter the original first, the new value second, and the sign is handled for you: an increase comes out as +, a fall as −.

It does not answer two near-miss questions. "How many percentage points did it move?" is the job of the Percentage Points Calculator, which cares about the gap between two rates rather than the relative shift of two values. And "what is X% of Y?" is the reverse problem — feed that to the percentage tool instead. Keeping the three questions apart resolves most disputes about "wrong" growth numbers: they are usually right numbers compared the wrong way.

A worked example, step by step

Problem: a café took 45,000 in revenue last quarter and 72,000 this quarter. What is the growth?

1. Difference: 72,000 − 45,000 = 27,000.
2. Base: the original value, 45,000 (not the new one).
3. Divide: 27,000 ÷ 45,000 = 0.6.
4. Convert: × 100 = +60%.
5. Sense-check: 60% of 45,000 is 27,000, exactly the gap — the speed number behaves.

Run the same inputs the other way — 72,000 down to 45,000 — and you get −37.5%, not −60%. Falling back is on a larger base, so the same money moves a smaller percentage. That asymmetry is not an error; it is the whole reason chart axes and announcements deserve a second look.

As a reference anchor: 100 growing to 150 and falling back to 100 are +50% and −33.33% (150 − 50 = 100, and the 100 you lose is a third of 300... actually one used a base of 150). Recompute mentally: 150 → 100 drops 50 on a base of 150, i.e. 33.33%. Two "opposite" rates that don't cancel — arithmetic working exactly as intended.

Reference table: moving from 60

Notice the pairs: +10% off and −10% back do not return to 60, they land at 54. Symmetry only exists in money units, never in percentages.

From the number to the decision

Three habits make a change figure survivable once it leaves the calculator. First, keep the base visible in the same sentence: "+60% on 45,000" and "+60% on 900" are different worlds, so the absolute detail line (27,000 here) should travel with the percentage. Second, preserve direction: a fall of 20% from 120 returns 96, not 100, so back-to-back +20% then −20% never returns you to the start line — symmetric rates describe asymmetric journeys. Third, if the growth spans several uneven periods, run this tool once per pair of periods rather than averaging them in your head: stacked rates on different bases are exactly where re-stacking goes wrong.

Finally, remember the audience. Executives ask "is that good?": the answer needs the base and the time window, not just the percent. Then, when the comparison crosses years, the CAGR Calculator annualises the same journey into one steady rate — the figure that makes unequal periods comparable — while this page stays the fast, honest instrument for one move between two values.

Mistakes that bend the change

• Zero (or empty) original. From 0 you cannot grow "relatively": the calculator rejects a zero base rather than inventing infinity.
• Swapping the base. (new − old) ÷ new reads confident and is wrong; growth always divides by the value you started from.
• Averaging two changes. +50% then −50% averages to 0% on paper but leaves you 25% poorer, because the second applies to a different base.
• Announcing points as percent. Interest from 4% to 5% is +1 percentage point and +25% relative — pick the phrasing before you hit send.
• Comparing spans that differ. +60% in three months and +60% in two years are different results that share a number; annotate time or annualise before concluding.

Keep exploring

• Percentage Points Calculator — express the same gap in percentage points.
• ROI Calculator — the same (final − start) ÷ start arithmetic, read as investment performance.
• CAGR Calculator — one steady yearly rate that smooths a multi-year change.
• Guide: How to Calculate Percentages.
• Guide: CAGR and Inflation Explained.