---
title: "Percentage Calculator: Change, Difference & Reverse"
description: "Calculate percentages, increases, decreases and reverse discounts. Compare percentage points and basis points with clear formulas and worked examples."
url: "https://worldcalculators.org/calculators/percentage/"
canonical: "https://worldcalculators.org/calculators/percentage/"
---

# Percentage calculator

Calculate percentages, increases, decreases and reverse discounts. Compare percentage points and basis points with clear formulas and worked examples.

## Choose the right percentage formula

First identify what is known and what is missing. A percentage of a number, a relative change and a rate difference answer different questions. These examples use the same calculation engine as the interactive tool.
|80 − 100| ÷ ((80 + 100) ÷ 2) × 100 = 22.22222222%

## Reverse percentage calculator: find the original

There are two common reverse-percentage questions. If you know a part and the percentage it represents, divide by the decimal percentage: 30 is 20% of 30 ÷ 0.20 = 150 . Choose “X is Y% of what?” to find this whole.
If you know a price after a discount, divide by the fraction that remains. An 80 price after 20% off represents 80% of the original, so the original is 80 ÷ 0.80 = 100 . Adding 20% back to 80 gives 96, which is why simply reversing the sign is incorrect.

## Percentage change versus percentage difference

Use percentage change for a before-and-after question: a salary, price or measurement moves from one value to another. It needs a non-zero starting value. Use percentage difference to compare two non-negative measurements on equal terms, dividing their absolute difference by their average.
For 80 and 100, the absolute difference is 20. Relative to the starting 80 it is 25%; relative to their average of 90 it is approximately 22.22%. Both calculations can be correct, but they describe different comparisons. State the denominator when reporting the result.

## Percentage points and basis points calculator

A rate changing from 4% to 5% rises by 1 percentage point , also called 100 basis points . Relative to the original rate, that is a 25% increase . Saying only “a 1% increase” would be ambiguous. The rate-difference mode displays the point change, basis points and relative change together.
One basis point is 0.01 percentage point. A change from 5% to 4.75% is −0.25 percentage points, or −25 basis points. This notation is useful for comparing interest rates, margins and other percentages without confusing an absolute rate difference with a relative change.

## Rounding and edge cases

Answers display up to ten significant digits and keep greater precision internally. A zero starting value makes relative change undefined. Two zeros also have no percentage difference under the average-denominator formula. The calculator explains these cases rather than showing infinity or keeping an old result.
Signed values are allowed where the formula supports them. For negative starting values, percentage change uses the absolute starting value as its base. State that convention when comparing losses, deficits or other signed quantities; percentage language can otherwise be misleading.

## Sources & Methodology

Arithmetic modes use a shared tested engine. The formulas and worked examples are visible, including denominator restrictions and the signed-change convention.
Standards and figures reviewed 9 September 2026.

Source: https://worldcalculators.org/calculators/percentage/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.