Percentage Calculator

Percentages express a number as a fraction of 100 and are one of the most useful tools in everyday math. This calculator handles the three problems people search for most: finding a percentage of a number ("What is 20% of 150?"), expressing one number as a percentage of another ("20 is what percent of 150?"), and calculating percentage change between two values ("What is the percent change from 80 to 100?").

The first mode uses the formula (X / 100) × Y. So 20% of 150 is (20 / 100) × 150 = 30. This is useful for tips, taxes, discounts, and commission calculations. Many shoppers use percentage-of math at the till to confirm a sale price, and freelancers use it to compute service taxes.

The second mode answers "X is what percent of Y?" using the formula (X / Y) × 100. So 20 is (20 / 150) × 100 ≈ 13.33% of 150. This shows up when you want to convert a raw fraction to a percentage — for example, "I scored 42 out of 50, what is that as a percentage?"

The third mode computes percent change with the formula ((New − Old) / Old) × 100. A positive result is an increase; a negative result is a decrease. This is the right formula for things like "my salary went from $60,000 to $66,000, that is a 10% increase" or "the stock dropped from $50 to $40, a 20% loss." Be careful: a 50% loss requires a 100% gain to recover, because the base value has changed. This calculator updates results instantly as you type, so you can play with values and build intuition.

Percentages also underpin almost every financial decision you make. Interest rates on loans, savings, mortgages and credit cards are quoted as annual percentages. Investment returns, inflation, salary raises, tax brackets and tip amounts are all expressed in percentage form. Once you internalise the three modes in this calculator, you stop second-guessing yourself at checkout, you can sanity-check a quote from a contractor on the spot, and you can rebalance a household budget in minutes instead of hours.

A common mistake is to confuse percentage points with percentages. A change from 4% to 6% is a 2 percentage-point increase, but it is a 50% relative increase. Newspapers blur this distinction constantly when reporting on interest rates, polls and unemployment. When you use this calculator, choose the mode that matches the wording of the question — "percent change" for relative shifts, "X of Y" for portions, and "X is what percent" for raw ratios. Reading the question carefully prevents costly errors.

Compound percentages behave very differently from simple ones. A 10% gain followed by a 10% loss does not return you to the starting point — you end up 1% down, because the second 10% is taken from a larger base. This asymmetry matters for stock returns, weight-loss tracking and any quantity that fluctuates. Use the percent-change mode on each step to see the cumulative effect, and remember that recovering from a loss always requires a larger percentage gain than the loss itself.

Mental math shortcuts make percentage calculations even faster. Ten percent of any number is found by moving the decimal one place to the left. One percent moves it two places. Half of either gives you 5% and 0.5%. Adding these building blocks lets you estimate almost any percentage in your head — 18% is roughly 10% + 5% + 3%, which is close enough for tipping or quick sanity checks. Use the calculator for precision and your head for ballpark figures.