Six types of percentage calculations — all with step-by-step solutions. Includes GST, tips, discounts, and percentage change.
To find a percentage of a number, divide the percentage by 100 and multiply by the number. For example, 20% of 150 = (20 ÷ 100) × 150 = 30. To find what percentage one number is of another, divide the first by the second and multiply by 100. This calculator handles percentage of a number, increase, decrease, change, difference and percent off — each with a step-by-step solution.
Every percentage problem uses one of three core relationships between the part, the whole and the percentage.
Increase and decrease measure how much a value has gone up or down, expressed as a percentage of the original.
These everyday percentages, decimals and fractions are worth knowing at a glance.
| Percentage | Decimal | Fraction |
|---|---|---|
| 10% | 0.10 | 1/10 |
| 20% | 0.20 | 1/5 |
| 25% | 0.25 | 1/4 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
These sound similar but answer different questions. Change has a direction (from an original value); difference compares two values symmetrically.
| Type | Formula | Use When |
|---|---|---|
| Percentage change | ((new − old) ÷ old) × 100 | There is a clear "before" value |
| Percentage difference | (|A − B| ÷ ((A + B) ÷ 2)) × 100 | Comparing two values with no "before" |
| Percentage off | original × (percent ÷ 100) | Working out a discount amount |
| Type | Formula |
|---|---|
| X% of Y | = (X ÷ 100) × Y |
| X is what % of Y | = (X ÷ Y) × 100 |
| X is Y% of what | = X ÷ (Y ÷ 100) |
| % Increase | = (New − Old) ÷ Old × 100 |
| % Decrease | = (Old − New) ÷ Old × 100 |
| Add GST (10%) | = Amount × 1.10 |
| Remove GST (10%) | = Amount ÷ 1.10 (or Amount × 10/11) |
Here are common real-world increase and decrease scenarios at a glance.
| Scenario | Calculation | Result |
|---|---|---|
| Salary raised from $75,000 to $82,500 | (82,500 − 75,000) ÷ 75,000 × 100 | +10% increase |
| Item discounted from $200 to $150 | (200 − 150) ÷ 200 × 100 | 25% decrease |
| Property up from $650k to $715k | (715,000 − 650,000) ÷ 650,000 × 100 | +10% increase |
Australia's 10% GST is one of the most common percentage calculations in business:
| Task | Method | Example ($100 ex-GST) |
|---|---|---|
| Add 10% GST to price | Price × 1.1 | $100 × 1.1 = $110 |
| Extract GST from price | Price ÷ 11 | $110 ÷ 11 = $10 GST |
| Find ex-GST price | Price ÷ 1.1 | $110 ÷ 1.1 = $100 |
(percent ÷ 100) × number(X ÷ Y) × 100((new − old) ÷ old) × 100((old − new) ÷ old) × 100original × (percent ÷ 100)× 1.XX Fast subtract %: × 0.XX
1) 20 2) 20 3) 25% 4) 44 5) $10 off → $40
1) (150−120)/120 × 100 = 25% 2) (250−200)/250 × 100 = 20% 3) |40−60| ÷ 50 × 100 = 40% 4) 68 ÷ 0.85 = $80 5) 1.25 × 0.75 = 0.9375 = 93.75%
What is a percentage?
A percentage is a way of expressing a number as a fraction of 100. The symbol % means 'per hundred.' For example, 25% means 25 out of every 100, or equivalently 0.25 as a decimal, or 1/4 as a fraction. Percentages are used to compare quantities, express change, and describe proportions.
How do you calculate a percentage increase?
Percentage increase = (New Value − Old Value) ÷ Old Value × 100. Example: a salary increasing from $70,000 to $77,000 is an increase of $7,000. $7,000 ÷ $70,000 × 100 = 10% increase. If the new value is lower than the old value, the result is negative, indicating a percentage decrease.
What is the difference between percentage change and percentage difference?
Percentage change is directional — it measures change from a starting value to an ending value. Percentage difference measures the difference between two values without a directional reference, using their average as the denominator: |A − B| ÷ ((A + B)/2) × 100. Use percentage change when comparing before and after; use percentage difference when comparing two independent values.
How is percentage used in Australian tax calculations?
Percentages are used in Australian calculations such as GST, income tax rates, the Medicare levy and student-loan repayments. These rates and thresholds may change, so use the relevant MegaCalcOnline income tax calculator or GST calculator, or current Australian Taxation Office guidance, for an up-to-date calculation.
How do you convert between percentage, decimal, and fraction?
To convert percentage to decimal: divide by 100 (25% = 0.25). To convert decimal to percentage: multiply by 100 (0.25 = 25%). To convert percentage to fraction: write over 100 and simplify (25% = 25/100 = 1/4). To convert fraction to percentage: divide numerator by denominator and multiply by 100 (3/4 = 0.75 = 75%).
How do I calculate a percent off a price?
To calculate percent off, multiply the price by the percentage and subtract it. For 20% off $50: 50 × 0.20 = $10, so the price becomes $40. This percent calculator does percent-off, percentage-of, and percent-difference calculations for you.
How do you calculate the percentage of a number?
Divide the percentage by 100 to get a decimal, then multiply by the number. For example, to find 30% of 200: 30 ÷ 100 = 0.30, then 0.30 × 200 = 60. So 30% of 200 is 60. The calculator above does this instantly and shows the steps.
How do you calculate percentage decrease?
Subtract the new value from the original, divide by the original, then multiply by 100. For example, from 100 to 75: (100 − 75) ÷ 100 × 100 = 25% decrease. The formula is the same as increase, just measuring a drop from the starting value.
How do you find what percentage one number is of another?
Divide the first number by the second, then multiply by 100. For example, 45 out of 60 is 45 ÷ 60 × 100 = 75%. This tells you what share the first number represents of the second, which is useful for test scores, completion rates and proportions.
Why is the percentage formula useful in everyday life?
Percentages appear everywhere — discounts, tips, tax and GST, interest rates, test scores, statistics and price changes. Knowing how to calculate a percentage of a number, a percentage increase or decrease, and a percentage change helps you compare values fairly and make quick, informed decisions.