Percentage Calculator
Comprehensive percentage calculator: percent of, percent change, increase/decrease by percent.
Free · Runs in your browser · No signup
Examples to try
Modes
Percent of · is what percent · percent change · increase by · decrease by. Pick a mode, then enter X and Y.
Common mistakes
- Using the wrong mode for the question wording.
- Confusing percentage points with percent change.
- Swapping old/new values on percent change.
Scope: Multi-mode percent math for school and daily life. Simpler ratios: percentage helper.
How to Use
Enter your values in the fields above and click Calculate to get instant results. All computations run locally in your browser. No data is ever uploaded or stored.
Related Calculators
Three Core Percentage Operations
This calculator handles the three distinct percentage questions people ask most often — each with its own formula.
"What is X% of Y?" → X / 100 × Y
"X is what percent of Y?" → (X / Y) × 100%"Percent change from X to Y?" → ((Y − X) / X) × 100%
Percent change is asymmetric: going from 100 to 150 is +50%, but returning from 150 to 100 is −33.3%.
Percentage Points vs. Percent Change
Percentage-point change: A rate going from 5% to 7% = 2 percentage points
Relative percent change: (7 − 5) / 5 = 40% increase
This distinction matters in news and finance: "interest rates rose 1%" usually means 5% → 6% (1 point), not 5% → 5.05%. A 200% gain means the value triples. A 100% loss means it goes to zero.
Advanced Percentage Calculations
This percentage calculator handles five distinct operations: finding a percentage of a number, determining what percentage one number is of another, calculating percentage change, and increasing or decreasing a value by a percentage. These operations cover virtually every percentage scenario you will encounter in daily life, academics, and professional work.
Three Core Percentage Calculations
Type 1 — Finding a percentage of a number: Multiply the number by the percentage and divide by 100. Formula: Result = Value x (Percentage / 100). Example: 18% of 250 = 250 x 0.18 = 45.
Type 2 — Finding what percentage one number is of another: Divide the part by the whole and multiply by 100. Formula: Percentage = (Part / Whole) x 100. Example: 37 is what percent of 200? (37 / 200) x 100 = 18.5%.
Type 3 — Percentage change: Subtract the old value from the new, divide by the old value, and multiply by 100. Formula: Change = ((New - Old) / Old) x 100. Example: Stock price went from 80 to 100: ((100 - 80) / 80) x 100 = 25% increase.
Real-World Examples
Shopping discounts: A jacket originally priced at 120 dollars is on sale for 30% off. Discount = 120 x 0.30 = 36 dollars. Sale price = 120 - 36 = 84 dollars. Alternatively, 30% off means you pay 70%, so 120 x 0.70 = 84 dollars directly.
Restaurant tips: Your dinner bill is 65 dollars and you want to leave an 18% tip. Tip = 65 x 0.18 = 11.70 dollars. Total = 65 + 11.70 = 76.70 dollars. For quick mental math, 10% of 65 is 6.50, and 8% is roughly half of that plus a bit, so approximately 5.20, totaling about 11.70.
Tax calculations: An item costs 45 dollars and sales tax is 8.5%. Tax = 45 x 0.085 = 3.83 dollars. Total = 48.83 dollars. When comparing prices across states with different tax rates, use percentage calculations to determine the real cost difference.
Percentage Change Formula
The percentage change formula is one of the most widely used calculations in business and finance: ((New Value - Old Value) / Old Value) x 100. A positive result indicates an increase; a negative result indicates a decrease. Common applications include measuring investment returns, comparing monthly expenses, tracking weight loss progress, and analyzing year-over-year business growth. Always note whether the change is relative to the old value (most common) or the new value, as this affects interpretation.
Percentage vs. Percentage Points
This distinction causes frequent confusion. If an interest rate rises from 5% to 7%, that is a 2 percentage point increase, but a 40% increase in the rate itself ((7-5)/5 x 100). In finance and statistics, the distinction is critical. Interest rate changes are typically quoted in percentage points, while stock price changes use percentages. Confusing the two can lead to significant misinterpretation of data.
Common Mistakes to Avoid
- Wrong base for percentage change: Always divide by the original value, not the new one. Going from 50 to 100 is a 100% increase, not 50%.
- Confusing "percent of" with "percent off": 20% of 80 dollars is 16 dollars; 20% off 80 dollars means you pay 64 dollars.
- Compounding percentages incorrectly: two consecutive 10% increases do not equal a 20% increase — they equal 21% (1.10 x 1.10 = 1.21).
- Forgetting that percentages are reversible in one direction only: if a price increases by 25% to reach 100, the original was 80 (not 75). To undo a 25% increase, you need a 20% decrease.
See CalcSolver's percentage helper for quick single-purpose calculations, the discount calculator for shopping scenarios, and the sales tax calculator for tax-inclusive pricing.
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Frequently Asked Questions
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. Example: What percent is 30 of 200? (30 / 200) x 100 = 15%.
How do I calculate percentage increase or decrease?
Percentage change = ((New - Old) / Old) x 100. If rent went from $1,200 to $1,350: (($1,350 - $1,200) / $1,200) x 100 = 12.5% increase.
How do I find a percentage of a number?
Multiply the number by the percentage and divide by 100. Example: 15% of 200 = 200 x 15 / 100 = 30.
What is the difference between percentage and percentage points?
A percentage point is the arithmetic difference between two percentages. If a rate goes from 5% to 7%, that is a 2 percentage point increase but a 40% increase relative to the original rate. The distinction is critical in finance and statistics.
How do I calculate a reverse percentage?
If you know the final value and the percentage change, find the original by dividing: Original = Final / (1 + Change/100). For example, if a price after 20% increase is $120, the original was $120 / 1.20 = $100.
How do I calculate successive percentage changes?
Multiply the factors together. Two consecutive 10% increases: 1.10 x 1.10 = 1.21, a 21% total increase (not 20%). This is because the second increase applies to the already-increased value.