Percentage Calculator

The three percentage questions people actually ask

Almost every percentage problem collapses into one of three forms. This calculator has a section for each:

• "What is X% of Y?" — the shopping‑discount question. Formula: result = Y × X / 100. Example: 20% off a £45 shirt → 20 × 45 / 100 = £9 discount, so you pay £36.
• "X is what % of Y?" — the score or share question. Formula: result = X / Y × 100. Example: you got 38 out of 50 on a test → 38 / 50 × 100 = 76%.
• "What's the % change from X to Y?" — the trend question. Formula: result = (Y − X) / X × 100. Example: salary went from £40,000 to £44,000 → (44−40) / 40 × 100 = 10% rise.

The gotcha almost everyone gets wrong

If something goes up by 50% and then down by 50%, you do not end up where you started. Start with 100 → +50% = 150 → −50% of 150 = 75. You're down 25%. The reason: percentage changes are multiplicative, and each one is taken from the new base, not the original. This trips up investors, dieters, and anyone tracking week‑over‑week stats. If you want to undo a 50% rise, you actually need a 33.3% fall. If you want to undo a 20% fall, you need a 25% rise.

Percentage points vs percent

If interest rates go from 2% to 3%, that's a rise of one percentage point, not "1% higher". In relative terms it's actually a 50% increase (3 is 50% more than 2). News stories get this wrong constantly. When you compare two percentages, always be specific: are you measuring the absolute gap (points) or the relative change (percent)?

Real‑world uses

• Shopping — "30% off" plus "extra 20% at checkout" isn't 50% off; it's 44% off (0.7 × 0.8 = 0.56).
• Tips — for a 15% tip on a $42 bill, use "What is 15% of 42?" → $6.30.
• Grades — "X is what % of Y" to see your test score as a percentage.
• Salary negotiations and rent rises — "% change from X to Y" to see a raise or a hike in honest terms.
• Fitness and weight loss — "% change" to report progress week‑over‑week without the rounding noise that raw kilograms produce.

Precision

The calculator uses JavaScript's 64‑bit IEEE‑754 floats, which is the same arithmetic your spreadsheet uses. That means it's exact for sensible numbers but has a tiny rounding error for some edge cases (0.1 + 0.2 is famously 0.30000000000000004). Results are displayed rounded for readability. For money, always round to two decimal places yourself when reporting figures — don't let floating‑point artifacts travel into a contract.