How percentage increase is calculated
A percentage increase measures how much a value has grown relative to its original amount. It is always expressed relative to the starting value — not the ending value — which is a common source of confusion.
% increase = ((New value − Original) ÷ Original) × 100 Example: 100 → 125 → ((125 − 100) ÷ 100) × 100 = +25% New value = Original × (1 + Percentage ÷ 100) Example: 100 increased by 25% → 100 × 1.25 = 125 Common percentage increase reference
| % Increase | Multiplier | 100 becomes | 200 becomes |
|---|---|---|---|
| 5% | × 1.05 | 105 | 210 |
| 10% | × 1.10 | 110 | 220 |
| 15% | × 1.15 | 115 | 230 |
| 20% | × 1.20 | 120 | 240 |
| 25% | × 1.25 | 125 | 250 |
| 50% | × 1.50 | 150 | 300 |
| 75% | × 1.75 | 175 | 350 |
| 100% | × 2.00 | 200 | 400 |
Formulas — both calculation modes
Find % change
Given an original value and a new value, the percentage change is the difference divided by the absolute original, multiplied by 100. A positive result is an increase; negative is a decrease.
% change = ((New − Original) ÷ |Original|) × 100 Original 800, New 1,000 → ((1000 − 800) ÷ 800) × 100 = +25% Original 1,000, New 750 → ((750 − 1000) ÷ 1000) × 100 = −25% Find new value
Given an original value and a percentage increase, multiply the original by 1 + (rate ÷ 100).
New value = Original × (1 + Percentage ÷ 100) Original 1,000 increased by 25% → 1,000 × 1.25 = 1,250 Original 500 increased by 7.5% → 500 × 1.075 = 537.50 Scientific notation is supported
Both input fields accept standard scientific notation. This is useful when working with very large or very small numbers — you can type 1e6 instead of 1000000, or 5e-3 instead of 0.005. The calculator reads these exactly as JavaScript's Number() does.
| You type | Interpreted as | Example — 25% increase |
|---|---|---|
| 1e3 | 1,000 | 1,000 → 1,250 |
| 2.5e2 | 250 | 250 → 312.50 |
| 1e6 | 1,000,000 | 1,000,000 → 1,250,000 |
| 5e-1 | 0.5 | 0.5 → 0.625 |
| 1.5e4 | 15,000 | 15,000 → 18,750 |
In the Find % change tab: entering 1e3 as both Original and New gives ((1,000 − 1,000) ÷ 1,000) × 100 = +0% — correct, because the value did not change. Entering 1e3 as Original and 1.25e3 as New gives +25%.
In the Find new value tab: entering 1e3 as Original and 25 as Percentage gives 1,000 × 1.25 = 1,250.
Frequently asked questions
Why is the result measured against the original, not the new value?
By convention, percentage change is always measured relative to the starting point. "A 25% increase from 100" means 25% of 100 — not 25% of the final value 125. Using the new value as the base would give a different (and less intuitive) number, and would make comparisons between different starting points inconsistent.
Can a percentage increase exceed 100%?
Yes. A 100% increase means the value doubled. A 200% increase means it tripled. A 1,000% increase means it is now 11 times the original value. There is no ceiling on percentage increases.
If I increase by 25% and then decrease by 25%, do I get back to the start?
No. Increasing 100 by 25% gives 125. Decreasing 125 by 25% gives 93.75 — not 100. This is because the second 25% is calculated on the new, larger base. Percentage changes do not simply cancel each other out.
What is a negative result on the increase calculator?
A negative result means the value actually decreased. The calculator shows the true percentage change regardless of direction — a negative sign means the new value is lower than the original. You can also switch to Decrease mode using the toggle at the top.
Does this calculator support scientific notation?
Yes. You can enter values like 1e3 (= 1,000), 2.5e2 (= 250), 1.5e4 (= 15,000), or 5e-1 (= 0.5). Standard JavaScript scientific notation is accepted in both the Original and New value fields. This makes it practical for very large or very small values without counting zeros. The result is always displayed in standard decimal form.
Does this calculator store my inputs?
No. All calculations run in your browser. Nothing is sent to a server or saved anywhere.