Percentage Calculator
Percentage problems fall into three types, each requiring a different formula. Finding what percentage one number is of another: divide the part by the whole and multiply by 100 (e.g. 45 of 180 = 25%). Finding a percentage of a number: multiply the number by the percentage divided by 100 (e.g. 15% of 240 = 36). Finding the original value when you know the result and percentage: divide the result by the percentage and multiply by 100. A fourth common need is percentage change: subtract old from new, divide by old, multiply by 100 (positive = increase, negative = decrease). In everyday Australian life, percentages appear in GST (10% added to the ex-GST price), stamp duty estimates, home loan interest rates, retail discounts, tax bracket calculations, and investment returns. This calculator handles all four problem types simultaneously, showing the formula used for each so you understand the calculation rather than just the answer.
Quick reference: 1% = 0.01 · 10% = 0.1 · 50% = 0.5 · 100% = 1 · 200% = 2
Frequently Asked Questions
How do I calculate a percentage of a number?
To calculate a percentage of a number, divide the number by 100 to find 1%, then multiply by the percentage you want. For example, to find 15% of 200: first calculate 200 divided by 100 equals 2 (which is 1%), then multiply 2 by 15 to get 30. This is equivalent to multiplying the original number by the decimal form of the percentage (0.15 × 200 = 30).
What is the formula for percentage increase?
The formula for percentage increase is ((New Value minus Original Value) divided by Original Value) times 100. This gives you the relative change expressed as a percentage. For example, if something grows from $50 to $65, the increase is $15. Divide $15 by the original $50 (giving 0.30), then multiply by 100 to get a 30% increase. This formula works whether the values are dollars, kilograms, or any other unit.
How do I convert a fraction to a percentage?
To convert a fraction to a percentage, divide the numerator (top number) by the denominator (bottom number) to get a decimal, then multiply by 100. For example, to convert 3/4 to a percentage: divide 3 by 4 which equals 0.75, then multiply by 100 to get 75%. This means 3/4 is equivalent to 75% of 1. You can verify this by calculating 75% of 4 (which is 0.75 × 4 = 3), confirming the conversion is correct.
What is the difference between "percent" and "percentage points"?
A percent represents a relative change or ratio, while a percentage point represents an absolute difference between two percentage values. If interest rates rise from 3% to 4%, that is a 33% increase in relative terms (because 1 is one-third of 3), but only a 1 percentage point absolute change. In finance, when comparing investment returns or interest rates over time, percentage points are the meaningful measure. Mixing up these concepts can significantly misrepresent changes, particularly for small percentages or large base values.
How do I calculate percentage decrease?
The formula for percentage decrease is ((Original Value minus New Value) divided by Original Value) times 100. This is essentially the inverse of percentage increase. For example, if a price drops from $80 to $60, the decrease is $20. Divide $20 by the original $80 (giving 0.25), then multiply by 100 to get a 25% decrease. The key is using the original value as your denominator, not the new lower value.
What is 100% of a number?
100% of any number equals the number itself, because 100% literally means 100 out of 100, or the complete whole. If you have 100% of a pizza, you have the entire pizza. In mathematical terms, 100% converted to decimal form is 1, and multiplying any number by 1 leaves it unchanged. This is a useful reference point: 50% is half (0.5), 25% is a quarter (0.25), and 100% is the whole (1.0).
How do I find the original price before a discount?
To find the original price before a discount was applied, divide the discounted price by (1 minus the discount percentage as a decimal). For example, if you paid $80 after a 20% discount: $80 ÷ (1 − 0.20) = $80 ÷ 0.80 = $100. The difference between the original and discounted price is the amount you saved. This reverse calculation is useful for comparing deals and verifying discounts at checkout.