Percentage Calculator
Three percentage calculations in one tool: find a percentage of a number, figure out what percentage one number is of another, and calculate the percentage change between two values.
How It Works
Percentages appear in almost every financial context — discounts, tax rates, tips, interest, portfolio returns, and pay rises. This calculator covers the three most common percentage questions.
Mode 1 — X% of Y (percentage of a value):
Formula: Result = (X / 100) × Y
Example: What is 15% of $240?
Result = (15 / 100) × 240 = 0.15 × 240 = $36
This is used for calculating tips, sales tax, commission, discounts, and VAT.
Mode 2 — X is what percent of Y (percentage of total):
Formula: Percentage = (X / Y) × 100
Example: 36 is what percent of 240?
Percentage = (36 / 240) × 100 = 15%
Use this to find what share something represents: "My rent is $900, income is $4,500 — rent is 20% of income." Or on an exam: "I scored 72 out of 90 — what percentage is that?" (72/90 × 100 = 80%).
Mode 3 — Percent change from X to Y:
Formula: Change = ((Y − X) / |X|) × 100
If Y > X: percentage increase
If Y < X: percentage decrease
Example: A stock went from $50 to $68. Change = ((68 − 50) / 50) × 100 = 36% increase.
Example: A salary cut from $75,000 to $60,000. Change = ((60000 − 75000) / 75000) × 100 = −20% decrease.
The absolute value of X is used in the denominator so the formula handles negative starting values correctly (for example, a business whose profit moved from −$10,000 to +$5,000 shows a 150% improvement).
A common pitfall: a 50% increase followed by a 50% decrease does not return to the original value. $100 → +50% = $150 → −50% = $75. That is because the second 50% is applied to the new (larger) base. This asymmetry is why investment returns compound the way they do.
Frequently Asked Questions
How do I calculate a percentage increase?
Use Mode 3 (percent change). Enter the original value as X and the new value as Y. The result shows the percentage increase. For example, from $80 to $100: ((100 − 80) / 80) × 100 = 25% increase.
What is the difference between percentage points and percent?
Percentage points are the arithmetic difference between two percentages. If an interest rate rises from 3% to 5%, it increased by 2 percentage points. The percentage change in the rate itself is (5 − 3) / 3 × 100 = 66.7%. This distinction matters in finance and economics.
How do I find the original price before a discount?
If a discounted price is $85 after a 15% discount: original = discounted price / (1 − discount%) = 85 / 0.85 = $100. This is the reverse percentage calculation.
How do I calculate tax-inclusive price?
Multiply the pre-tax price by (1 + tax rate). For $200 with 8% tax: 200 × 1.08 = $216. To extract tax from an inclusive price: tax amount = price × (rate / (100 + rate)). For $216 at 8%: tax = 216 × (8/108) = $16.
How do percentage tips work?
Tip = bill amount × (tip % / 100). For a $75 bill with 20% tip: 75 × 0.20 = $15 tip, $90 total. A quick mental trick: move the decimal left one place to get 10%, then double for 20%. 10% of $75 = $7.50, doubled = $15.