Percentage Calculators
A percentage expresses a number as a fraction of 100. Percentage arithmetic covers dozens of everyday calculations — from working out a discount at a shop to measuring investment growth or tracking a salary increase. This guide covers every common percentage formula, with worked examples and direct links to each calculator.
All formulas on this page are verified against peer-reviewed mathematical sources. Each linked calculator uses the same verified formula with known-value test coverage.
Quick Percentage Calculator
Formulas at a Glance
| Type | Formula | Example |
|---|---|---|
| Percentage of a number | result = base × (rate ÷ 100) | 20% of 150 = 30 |
| What percent of | percent = (part ÷ whole) × 100 | 30 is 20% of 150 |
| Percentage change | change% = ((new − old) ÷ |old|) × 100 | 80 → 100 = +25% |
| Percentage increase | new = old × (1 + rate ÷ 100) | 80 + 25% = 100 |
| Percentage decrease | new = old × (1 − rate ÷ 100) | 100 − 20% = 80 |
| Discount price | price = original × (1 − discount% ÷ 100) | 200 at 15% off = 170 |
| Tip amount | tip = bill × (rate ÷ 100) | 15% of 80 = 12 |
| Markup price | selling = cost × (1 + markup% ÷ 100) | 50 cost + 40% = 70 |
Percentage of a Number
The most common percentage calculation: find a specific percentage of a given value. Used for calculating VAT, tax amounts, service charges, percentage-based bonuses, and commissions.
Formula: result = base_value × (rate ÷ 100)
Example 1: What is 15% of 240?
240 × (15 ÷ 100) = 240 × 0.15 = 36
Example 2: A 500 salary bonus at 8% performance uplift:
500 × 0.08 = 40 uplift → total = 540
What Percent Of
Find what percentage one number represents of another. Used for tracking progress toward a goal, expressing a part of a budget, or comparing a sub-group to a total.
Formula: percent = (part ÷ whole) × 100
Example 3: 45 students passed out of 180 enrolled. What percentage passed?
(45 ÷ 180) × 100 = 25%
Example 4: You spent 350 of a 500 monthly budget. How much remains as a percentage?
spent: (350 ÷ 500) × 100 = 70% → 30% remaining
Percentage Change
Measures the relative change between an old value and a new value. Returns a positive number for an increase and a negative number for a decrease. Widely used in finance, economics, and performance tracking.
Formula: change% = ((new − old) ÷ |old|) × 100
Example 5: A product price rises from 80 to 96. What is the percentage change?
((96 − 80) ÷ 80) × 100 = (16 ÷ 80) × 100 = +20%
Note: Percentage increases and decreases are not symmetrical. A 20% increase followed by a 20% decrease does not return to the original value — each percentage applies to a different base.
Percentage Increase & Decrease
Calculate a new value after applying a percentage increase or decrease to an original. Used for salary raises, price hikes, cost reductions, and population growth.
Increase formula: new = old × (1 + rate ÷ 100)
Decrease formula: new = old × (1 − rate ÷ 100)
Example 6: A salary of 32,000 increases by 7.5%:
32,000 × 1.075 = 34,400
Example 7: A product costing 120 is reduced by 30%:
120 × (1 − 0.30) = 120 × 0.70 = 84
Discount Calculator
Find the sale price and saving from a percentage discount. Used for retail, e-commerce, and promotional pricing. The discount amount equals the original price multiplied by the discount rate.
Formula: sale price = original × (1 − discount% ÷ 100)
Example 8: A 399 laptop is discounted by 35%:
saving = 399 × 0.35 = 139.65 → sale price = 259.35
Tip Calculator
Calculate the tip amount and total bill from a bill value and tip percentage. Optionally split the total across multiple diners.
Formula: tip = bill × (rate ÷ 100) ; total = bill + tip
Example 9: 67.50 restaurant bill, 15% tip, 4 diners:
tip = 67.50 × 0.15 = 10.13 → total = 77.63 → per person: 19.41
Related Calculators
- Percentage of Number Calculator — Find a percentage of any number. Example: 10% of 200 = 20.
- What Percent Of Calculator — Find what percentage one number is of another. Example: 25 is 25% of 100.
- Percentage Change Calculator — Calculate percentage increase or decrease between two values.
- Discount Calculator — Calculate discounted prices and savings from a percentage discount.
- Tip Calculator — Calculate tip amounts and totals from bill amount and tip percentage.
Frequently Asked Questions
- What is the formula for finding a percentage of a number?
- Multiply the base value by the rate divided by 100. Formula: result = base × (rate ÷ 100). For example, 20% of 150 is 150 × 0.20 = 30. Use the Percentage of Number Calculator for instant results.
- How do I calculate percentage change between two numbers?
- Subtract the old value from the new value, divide by the old value, then multiply by 100. Formula: change% = ((new − old) ÷ old) × 100. A positive result is an increase; negative is a decrease. For example, from 80 to 100: ((100 − 80) ÷ 80) × 100 = 25%.
- What is the difference between percentage increase and percentage change?
- Percentage change is the general formula covering both increases and decreases. Percentage increase specifically measures the positive growth relative to an original value. The formula is the same — (new − old) ÷ old × 100 — but 'percentage increase' implies the result is positive. Use the Percentage Change Calculator to handle both cases.
- Why do a 25% increase then a 25% decrease not return to the original value?
- Because each percentage is calculated on a different base. A 25% increase on 100 gives 125. A 25% decrease on 125 gives 93.75 — not 100. This asymmetry is a fundamental property of percentage arithmetic. It is not a calculation error.
- How do I find what percentage one number is of another?
- Divide the part by the whole and multiply by 100. Formula: percent = (part ÷ whole) × 100. For example, 30 is what percent of 150? 30 ÷ 150 × 100 = 20%. Use the What Percent Of Calculator for instant results.
- How do I calculate a discount percentage given an original and sale price?
- Divide the discount amount by the original price, then multiply by 100. Formula: discount% = ((original − sale) ÷ original) × 100. For example, a product originally priced at 80 is on sale for 60: ((80 − 60) ÷ 80) × 100 = 25% discount. Use the Discount Calculator to find the sale price from a percentage off.
- What is the difference between markup and margin?
- Markup is profit expressed as a percentage of cost price. Margin is profit expressed as a percentage of selling price. For a product costing 80 that sells for 100: markup = (20 ÷ 80) × 100 = 25%; margin = (20 ÷ 100) × 100 = 20%. Both use the same 20 profit but different bases.
Source & Methodology
All percentage formulas on this page are verified against the following tier-1 sources:
- NIST Handbook of Mathematical Functions — National Institute of Standards and Technology. Provides the authoritative mathematical definitions for ratios and percentage calculations.
- Khan Academy: Percentages — peer-reviewed educational reference for percentage arithmetic including change, increase, and decrease formulations.
- OpenStax Prealgebra, 2nd edition — open-access academic textbook, Chapter 6 (Percents). Provides worked derivations for percentage of a number, percentage change, and reverse percentage formulas.
Each linked calculator uses known-value test cases that are run on every build to verify formula correctness.