Percentage Calculator

The three percentage problems everyone encounters

Most percentage questions fall into one of three types, and once you can recognize which type you're dealing with, the math is straightforward. This calculator handles all three — but understanding what's happening is useful when you're doing quick mental math in a store, at work, or in a negotiation.

• Type 1: What is X% of Y? (Finding a part) — "What is 15% of $85?"
• Type 2: X is what percent of Y? (Finding the rate) — "What percentage of 80 is 24?"
• Type 3: X is Y% of what? (Finding the whole) — "35 is 25% of what number?"

Each type uses a different rearrangement of the same relationship: Part = Whole × (Percent ÷ 100).

How to calculate percentage of a number

This is Type 1: What is X% of Y? Multiply Y by (X ÷ 100). A couple of shortcuts make this fast in your head:

• 10%: Move the decimal one place left. 10% of $74 = $7.40.
• 5%: Calculate 10%, then halve it. 5% of $74 = $3.70.
• 15%: Add 10% + 5%. 15% of $74 = $7.40 + $3.70 = $11.10. (Useful for tips.)
• 20%: Calculate 10%, then double it. 20% of $74 = $14.80.
• 1%: Move decimal two places left. 1% of $74 = $0.74. Scale up from there.

Finding what percentage one number is of another

This is Type 2: X is what percent of Y? Divide X by Y, then multiply by 100. "24 is what percent of 80?" → 24 ÷ 80 = 0.30 × 100 = 30%.

This comes up constantly in real life: your test score (17 out of 23 correct → 73.9%), a discount ("I saved $32 on a $120 item → I saved 26.7%"), or a business metric ("We closed 14 of 67 leads → 20.9% conversion rate").

Percentage change: increase and decrease

Percentage change measures how much something grew or shrank relative to where it started:

If your rent went from $1,400 to $1,575: change = ((1,575 − 1,400) ÷ 1,400) × 100 = 12.5% increase. If a stock fell from $84 to $71: change = ((71 − 84) ÷ 84) × 100 = −15.5% decrease.

One thing to watch: a 50% drop followed by a 50% gain doesn't get you back to even. If something falls from $100 to $50 (−50%), a 50% gain on $50 only gets you to $75, not $100. You'd need a 100% gain to recover from a 50% loss. This asymmetry is why protecting against big losses matters more than chasing big gains.

Percentage points vs percentages — a critical distinction

This is where a lot of misleading statistics live, and it's worth being clear on. If an interest rate rises from 2% to 3%, that's a 1 percentage point increase. But it's a 50% increase in rate. Both statements are accurate. People use whichever sounds better for their argument.

Similarly, if a poll shows a candidate's approval going from 40% to 44%, their approval rose by 4 percentage points — but it rose by 10% relative to where it was. Politicians and pundits mix these up (sometimes intentionally) all the time.

Where percentages trip people up most

A few common places where the math surprises people:

• Sequential discounts don't add up: A 20% discount followed by an additional 15% off is not 35% off. It's 20% off, then 15% off the already-reduced price: 1 − (0.80 × 0.85) = 32% total discount.
• Tip math: Most people calculate 20% tip on the pre-tax total, not the final bill. On a $90 meal with $8 tax, 20% of $90 = $18. 20% of $98 = $19.60. The difference is small but worth knowing the convention.
• Sales tax: A "10% tax" on a $50 item makes it $55. If you're trying to back out the pre-tax price from $55: divide by 1.10, not subtract 10%. 55 ÷ 1.10 = $50. Subtracting 10% of $55 gives you $49.50 — wrong.
• Investment fees: A "small" 1.5% annual expense ratio on an investment account doesn't just cost 1.5% of your money — over 30 years, it can reduce your ending balance by 25–30% compared to a 0.05% fee. Percentages compound just like returns do.