Percentage Calculator
Calculate the percentage of a number, percentage change, increase or decrease, and reverse percentage — with clear formulas.
What is % Percent of the Number? (Also shows the increased and decreased values.)
What percent of the Whole is the Part? (e.g. 250 is 50% of 500.)
What is the change (increase or decrease) from the Old Value to the New Value?
What is the original (pre-increase) value of a number whose value increased by % Percent is the Amount? (e.g. removing tax)
How to Calculate a Percentage? The Basic Formula
Percentage calculation is the most common way to express the ratio of a number within a whole. The word "percent" comes from the Latin "per centum", meaning "per hundred". The basic percentage formula is:
Result = Number × Percent ÷ 100
For example, 20% of 500: 500 × 20 ÷ 100 = 100. In everyday life, price discounts, raise rates, exam success percentages, tax calculation and statistics all rely on this basic formula.
Percentage Formulas (All Modes)
There are six core scenarios for percentage calculations. The formula and an example for each are below:
| Calculation Type | Formula | Example |
|---|---|---|
| Y% of X | X × Y ÷ 100 | 25% of 800 = 200 |
| X as % of Y | (X ÷ Y) × 100 | 150 is 25% of 600 |
| Percentage increase | ((New − Old) ÷ Old) × 100 | 1,000 → 1,250 = +25% |
| Percentage decrease | ((Old − New) ÷ Old) × 100 | 1,200 → 900 = −25% |
| Net from Z incl. Y% | Z ÷ (1 + Y / 100) | 1,200 incl. 20% → Net 1,000 |
| If Z = Y% of X, find X | Z × 100 ÷ Y | 120 = 15% of X → X = 800 |
How to Calculate Percentage Increase
Percentage increase shows proportionally how much a value has grown. It is used for price rises, salary raises, population growth or stock returns.
Formula: Percentage Increase = ((New Value − Old Value) ÷ Old Value) × 100
- If a salary rises from 25,000 to 32,500: ((32,500 − 25,000) ÷ 25,000) × 100 = 30% increase
- If rent rises from 15,000 to 18,000: ((18,000 − 15,000) ÷ 15,000) × 100 = 20% increase
If the result is negative, it means a percentage decrease. The "Change Rate" mode shows the percentage change, absolute difference and formula automatically when you enter the start and end values.
What Percent Is One Number of Another?
To find what percent a part is of a whole, use the formula (Part ÷ Whole) × 100. This is useful for exam scores, market share, budget ratios and progress tracking. For example, scoring 75 out of 300 means (75 ÷ 300) × 100 = 25%. The "What Percent" mode does this instantly and also shows the remaining percentage.
Reverse Percentage and Removing Tax
Reverse percentage answers questions like "what was the price before tax?". When a total already includes a percentage (such as sales tax), the net amount is found with Net = Total ÷ (1 + Percent/100). For a total of 1,200 including 20%: 1,200 ÷ 1.20 = 1,000, and the included portion is 200. The "Reverse" mode handles both removing an added percentage and finding the whole from a known partial value.
Calculating Discount Percentages
Discounts are one of the most common everyday uses of percentages. The discount amount equals Old Price × Discount% ÷ 100, and the discounted price equals Old Price × (1 − Discount%/100). For example, a 30% discount on 800 gives 800 × 0.70 = 560, saving 240. Use the "% of a Number" mode to find the discount amount, or the "Change Rate" mode to find the discount percentage between two prices.
How to Calculate Percentage: Step by Step
If you are wondering how to calculate percentage by hand, follow these simple steps — or let our simple percentage calculator do the math for you:
- Identify what you have and what you need: a number and a percent, two numbers to compare, or an old and new value.
- Pick the matching mode: "% of a Number", "What Percent", "Change Rate" or "Reverse".
- Apply the formula: for a percent of a number, multiply the number by the percent and divide by 100.
- Read the result: the tool shows the answer, the formula used and the remaining percentage where relevant.
For example, to find 15% of 240: 240 × 15 ÷ 100 = 36. This automatic percentage calculator performs every step for you, so you never have to remember the formula.
Percentage Increase and Decrease Calculator
The percentage increase calculator and percentage decrease calculator both live in the "Change Rate" mode. Enter the old and new value and the tool returns the percentage change, the absolute difference and the direction (increase or decrease):
- Increase: 80 → 100 gives ((100 − 80) ÷ 80) × 100 = +25%.
- Decrease: 100 → 80 gives ((100 − 80) ÷ 100) × 100 = −20%.
Note that the same absolute change is a different percentage depending on the starting value — a common source of confusion that this percent calculator removes by always showing the base it used.
Common Mistakes in Percentage Calculation
Even with a percentage calculator, a few mistakes come up again and again. Watch out for these:
- Reversing increase and decrease: a 25% rise followed by a 25% fall does not return you to the start — 100 → 125 → 93.75.
- Confusing percent and percentage points: going from 10% to 12% is a 2 percentage-point rise, but a 20% relative increase.
- Removing a percentage wrongly: to remove an added 20% from a total you divide by 1.20, not subtract 20%.
- Using the wrong base: always divide the change by the original value, not the new one.
Which Mode Should I Use?
This percent calculator has four modes. Use the table below to pick the right one for your question:
| Your Question | Mode to Use |
|---|---|
| What is 20% of 500? | % of a Number |
| 150 is what percent of 600? | What Percent |
| Price went 1,000 to 1,250, what % change? | Change Rate |
| Total is 1,200 incl. 20%, what is net? | Reverse |
Common Uses of Percentage Calculation
| Use Case | How It Helps |
|---|---|
| Shopping & discounts | Find the final price after a percentage discount |
| Finance & raises | Calculate salary raise, interest or growth rates |
| Exams & grades | Convert scores into success percentages |
| Statistics | Express proportions and changes clearly |
You can find more information and examples in the frequently asked questions section below. Percentage calculation is one of the most useful everyday math skills — enter your values in the relevant mode and this free percentage calculator gives you the result with its formula instantly.
Frequently Asked Questions About the Percentage Calculator
Basic percentage formula: Result = Number × Percent ÷ 100. For example, 25% of 600 = 600 × 25 ÷ 100 = 150. In the tool above, choose the "% of a Number" mode and enter the number and percentage; the result and formula are shown automatically.
Percentage increase = ((New Value − Old Value) ÷ Old Value) × 100. For example, if a price rises from 1,000 to 1,300: ((1,300 − 1,000) ÷ 1,000) × 100 = 30% increase. A negative result means a decrease. Use the "Change Rate" mode to calculate automatically.
In the "Reverse" tab choose "Remove an added percentage". For a total of 1,200 including 20%: Net = 1,200 ÷ (1 + 20/100) = 1,000, tax = 200. The tool shows the result and formula automatically.
Use the "What Percent" mode. Formula: (Part ÷ Whole) × 100. For example, 75 is what percent of 300? (75 ÷ 300) × 100 = 25%. Useful for exam scores, market share or budget ratios.
Six core formulas: (1) Y% of X = X×Y÷100, (2) X as % of Y = (X÷Y)×100, (3) Increase = ((New−Old)÷Old)×100, (4) Decrease = ((Old−New)÷Old)×100, (5) Net from Z incl. Y% = Z÷(1+Y/100), (6) If Z is Y% of X then X = Z×100÷Y. The 4 modes cover all of them.
Discount amount = Old Price × Discount% ÷ 100. Discounted price = Old Price − Discount amount, or directly Old Price × (1 − Discount%/100). For example, 30% off 800: 800 × 0.70 = 560.
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