# Free online percentage change calculator

> Percentage change measures how much a value grew or shrank relative to its starting point. Choose a mode to find the change, the new value, or the original value.

Calculate percentage change between two values, find the new value after a percentage increase or decrease, or work backwards to find the original value.

**Interactive version:** https://onlinecalculator.me/math/percentage-change/
**Category:** Math

## How to use

1. Pick a mode: **% Change** (given old and new), **New Value** (given old and a percent), or **Original Value** (given new and a percent).
2. Enter the two known values.
3. The result, difference, and direction appear immediately.

## Formulas

**Percentage change** (mode: % Change)

```
% change = ((new − old) / |old|) × 100
```

**New value** (mode: New Value)

```
new = old × (1 + % / 100)
```

**Original value** (mode: Original Value)

```
old = new / (1 + % / 100)
```

## Worked examples

**Price drop:** a jacket cost $80 and now costs $68.
% change = ((68 − 80) / 80) × 100 = **−15%** (decrease)

**Salary raise:** starting salary $50,000, raise of 8%.
New = 50,000 × 1.08 = **$54,000**

**Reverse calculation:** a product sells for $115 after a 15% markup. Original price?
Original = 115 / 1.15 = **$100**

## Notes

- A negative percentage means the value decreased.
- If the original value is zero, percentage change is mathematically undefined; the calculator shows 0%.
- Results are rounded to four decimal places.

## Frequently asked questions

### How is percentage change calculated?

Percentage change = ((new − old) / |old|) × 100. A positive result is an increase; negative is a decrease.

### How do I find the new value after a percentage change?

New value = old × (1 + percent / 100). Example: 200 increased by 15% → 200 × 1.15 = 230.

### How do I find the original value if I know the new value and the percentage change?

Original = new / (1 + percent / 100). Example: the result is 230 after a 15% increase → 230 / 1.15 = 200.

### What is the difference between percentage change and percentage difference?

Percentage change always compares a new value to a defined starting point. Percentage difference divides by the average of both values and has no directional meaning.

### Can the percentage change exceed 100%?

Yes. If a value doubles, the percentage change is 100%. Tripling gives 200%, and so on. There is no upper limit.

### What happens when the original value is zero?

Division by zero makes the percentage change undefined. The calculator returns 0% and flags "no change" in that case.

## Sources

- [Relative change (percentage change)](https://en.wikipedia.org/wiki/Relative_change) — Wikipedia
- [Percent (percentage increase and change)](https://mathworld.wolfram.com/Percent.html) — Wolfram MathWorld

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