Percentage Calculator
Four percentage modes: X% of Y, X is what % of Y, percentage increase or decrease, and percent change between two numbers.
How to use this calculator
Pick the mode that matches the sentence you're trying to answer — "what is X% of Y?", "X is what % of Y?", "increase or decrease Y by X%", or "what's the percent change from A to B?". The inputs change to fit; switching modes preserves your numbers within each mode so you can compare answers.
The four sentences in plain English
Mode 1 — X% of Y:"What is 8.25% of $45?" answers a portion question. Useful for sales tax, commission, or any partial amount. Mode 2 — X is what % of Y:"$10 tip on a $45 bill is what percent?" answers a ratio question. Useful for working backwards from a known piece.
Mode 3 — increase/decrease Y by X%:"Increase $45 by 20%" gives the new total ($54) and the delta ($9). Useful for tips, taxes, raises, or markups. Mode 4 — percent change A → B:"From $45 to $50 is what % change?" answers an over-time-or-comparison question. Useful for growth rates, sale prices, statistics.
Why a 50% drop doesn't undo a 50% gain
Percent change is base-dependent. $100 up 50% = $150. $150 down 50% = $75 — not $100. To exactly cancel a +50% gain, you need a −33.3% drop (50/150 = 33.3%). This is why a stock down 20% needs a 25% rally to break even, and why crashes hurt portfolios more than equivalent rallies help. The calculator's mode 4 makes it easy to verify these.
Common pitfalls
Compounding vs. linear: a 10% increase followed by a 10% increase is +21%, not +20% — the second 10% is on the new larger base. This calculator does single-step changes; for compounded growth, see the compound interest calculator. Percentage points vs. percent: rates moving from 5% to 7% is a 2 percentage point change but a 40% percent change. The two are easy to confuse — be explicit when you communicate.
When to use each mode in everyday life
Sales: mode 3 to compute a discounted price, mode 4 to verify the discount rate matches what was advertised. Wages: mode 3 to apply a raise. Investing: mode 4 to compare returns across time periods. Cooking and recipes: mode 1 to scale a portion. Probability and statistics: mode 2 to convert an observed count into a percent.
Frequently asked questions
What's the difference between the four modes?▾
Mode 1 (X% of Y) computes a portion: 25% of 200 = 50. Mode 2 (X is what % of Y) computes the ratio: 50 is 25% of 200. Mode 3 (increase/decrease Y by X%) applies a one-shot adjustment: 100 increased by 10% = 110. Mode 4 (% change between two numbers) measures the difference: 100 to 150 is +50%. They look similar but answer different questions — pick the one whose sentence matches what you're trying to compute.
How is percent change computed?▾
Strict formula: (new − old) ÷ old × 100. Going from 100 to 150 is +50%. Going from 150 back to 100 is −33.3% — the percent depends on which number is the base, which is why a 50% drop doesn't undo a 50% gain. The calculator uses the strict mathematical definition; with negative starting values the sign of the result follows the math, not intuition.
Why are negative percents rejected in the increase/decrease mode?▾
To prevent ambiguity. "Increase by −10%" and "decrease by 10%" should mean the same thing, but it's easy to flip a sign and produce the opposite. Forcing a positive percent plus an explicit direction (increase or decrease) eliminates the class of bug. Use mode 4 (percent change) if you want a signed result.
What happens with a starting value of zero?▾
Modes 2 and 4 both involve dividing by the starting value, which is undefined when that value is zero — the calculator surfaces an error rather than returning Infinity or NaN. Modes 1 and 3 both work fine with a zero input (e.g., 25% of 0 = 0; 0 increased by anything is 0).
How do I compute a percentage tip or sales tax?▾
Use mode 3 (increase Y by X%). For a 20% tip on $45.50, enter 45.50 as the value, choose 'increase', and 20 as the percent — the result is the total ($54.60) and the delta is the tip itself ($9.10). Same flow works for sales tax: enter the pre-tax amount, choose increase, and enter the tax rate.
How accurate is the calculator at the limits?▾
It uses standard IEEE 754 double-precision floating point — about 15 significant digits. For everyday percentages (sale prices, tips, growth rates) accuracy is exact in the digits you care about. Extremely small or large values display with appropriate precision automatically; results aren't pre-rounded internally.
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