What percent did it grow? Prices, salaries, subscribers, waistlines — the question is always the same shape: compare the change to where you started. This percentage increase calculator works both ways: enter an old and a new value to get the percentage increase between them, or enter a starting value and a percentage to get the increased result. The formula is one line, but the starting-value discipline behind it is where most people slip — so the working is shown with every answer.
The Percentage Increase Formula
Percentage increase = (new value − old value) ÷ old value × 100. Three commitments hide in that line. The numerator is the change, not the new value. The denominator is the old value — where you started, never where you arrived. And the result is a percentage of the starting point, which is why the same 20-unit rise is +25 percent from 80 but only +4 percent from 500. The second mode of the calculator inverts the question: new value = old value × (1 + p/100).
Worked Example 1: A Price Rise
A jacket rises from 80 to 100. The change is 20; divided by the starting 80 that is 0.25, so the increase is 25 percent. Sanity-check from the other direction: 80 increased by 25 percent is 80 × 1.25 = 100 ✓. If a report claimed "prices rose 20 percent" here it would be dividing by the wrong base — the tell-tale error this formula exists to prevent.
Worked Example 2: Applying an Increase
A salary of 200 (thousand, or any unit) rises by 15 percent. Mode 2: 200 × 1.15 = 230, an increase of 30. Note the compounding trap for repeated years: two successive 15 percent rises are not 30 percent total but 1.15 × 1.15 = 1.3225, a 32.25 percent rise — percentages multiply through their factors, they do not add, whenever each applies to the new base.
Percentage Points Are Not Percent
When the thing changing is itself a percentage, language matters. An interest rate moving from 4 percent to 5 percent has risen by 1 percentage point — but by 25 percent relative to its starting level ((5 − 4) ÷ 4). News reports swap these constantly, and the two readings differ by a factor of 25 here. This calculator computes the relative change; if your source says "points," it means the plain subtraction.
Increases Above 100 Percent
An increase of 100 percent means the value doubled (the increase equals the whole starting value). Two hundred percent means it tripled — increase of twice the original plus the original. Beyond a few hundred percent, fold-language is clearer: "grew 10×" beats "increased 900 percent" (which is what 10× means: the increase is 9 times the original). The calculator's note prints the ×-factor alongside the percentage precisely for these cases.
Common Mistakes
Dividing by the new value instead of the old is the champion error: (100 − 80) ÷ 100 = 20 percent sounds tidy and is wrong. Adding successive percentages instead of compounding their factors is second. Third: reporting a percentage increase from a zero or negative base, where the measure breaks down — from −50 to +50 the formula gives a meaningless −200 percent; describe such swings in absolute terms. Finally, an increase and its reversing decrease are never equal percentages: up 25 percent then down 20 percent returns to the start, because the bases changed mid-journey.
Increases in the Wild: Reading Growth Claims
Every growth headline is a percentage-increase claim with a base chosen by the claimant. "Sales up 40 percent" from a tiny launch base may mean fewer units than a rival's "up 4 percent" on a mature product. The disciplined reader asks two questions: increase from what base, and over what period? With those two answers, this calculator reconstructs the underlying values — old value from new value and percentage (divide by 1 + p/100) — and the growth claim becomes checkable arithmetic instead of atmosphere.
Related Tools
The decrease side of the story is the Percentage Decrease Calculator, and the full family lives in the Math Calculators hub, including the Percentage Difference Calculator for base-free comparisons.
Frequently Asked Questions
How do you calculate percentage increase?
Subtract the old value from the new, divide by the old value, and multiply by 100. From 80 to 100: (100 − 80) / 80 × 100 = 25 percent.
Why do you divide by the old value and not the new one?
Because the increase is measured relative to where you started. The old value is the base the change grew from; dividing by the new value answers a different question (the decrease that would reverse the trip).
What is a 100 percent increase?
A doubling. The increase equals the entire starting value, so the result is twice the original. A 200 percent increase triples; 900 percent makes ten times.
How do I apply a percentage increase to a number?
Multiply by (1 + p/100). A 15 percent increase on 200 is 200 × 1.15 = 230 — use the calculator's apply mode.
What is the difference between percent and percentage points?
A rate going from 4 to 5 percent rises 1 percentage point (plain subtraction) but 25 percent in relative terms. Points compare percentages directly; percent compares them relative to the starting rate.
Can a percentage increase exceed 100?
Yes, without limit — unlike decreases, which are capped at 100 percent (a value cannot fall more than all of itself, down to zero). Increases of many hundreds of percent are common for small starting bases.
Do two 10 percent increases make 20 percent?
No — they compound: 1.10 × 1.10 = 1.21, a 21 percent total increase. Each rise applies to the enlarged base left by the previous one.