How to Calculate Percentage: Increase, Decrease & Discounts

You meet percentages a dozen times a day: the 15% tip on a restaurant bill, the 30% off jacket, the salary raise, the sales tax line. The good news is that every single one of these runs on one formula — and once it clicks, you can do most of this math in your head before the cashier finishes bagging.

This guide gives you that formula, then walks through the four situations where people actually use it: tips, increases, decreases, and discounts — with real numbers worked all the way through.

The one formula that runs everything

Percent literally means “per hundred.” So 20% is just 20 per 100, or the fraction 20/100. The master formula:

From that one line you get the two forms everyone actually uses day to day:

• Finding a percentage of a number: Part = (Percentage ÷ 100) × Whole. So 20% of 150 = 0.20 × 150 = 30.
• Finding what percent one number is of another: (30 ÷ 150) × 100 = 20%. Same relationship, just solved for a different side.

Notice the pattern: going between “percent” and “decimal” is just moving the decimal point two places. 20% ↔ 0.20, 7.5% ↔ 0.075. Internalize that move and the rest is arithmetic.

Worked example: a 15% tip on a $64 bill

The bill comes to $64. You want a 15% tip. Using the first form:

• Tip = 0.15 × 64 = $9.60
• Total = 64 + 9.60 = $73.60

Here’s the mental-math shortcut servers wish everyone knew: 10% of anything is just the decimal moved one place ($6.40), and 5% is half of that ($3.20). 15% = 10% + 5% = $9.60. Takes three seconds, no phone calculator, no fumbling.

Percentage increase: a raise from $65,000 to $72,000

Increases and decreases use the same formula, with a different starting point — and the starting point is where almost everyone slips up. The rule: always divide by the original (old) value.

Your salary goes from $65,000 to $72,000:

• Difference: 72,000 − 65,000 = $7,000
• Divide by the old salary: 7,000 ÷ 65,000 = 0.10769
• Times 100: 10.77% ≈ a 10.8% raise

This is the formula behind every “prices rose X%” headline. Gas went from $3.50 to $4.00 a gallon? (4.00 − 3.50) ÷ 3.50 × 100 = 14.3% increase — even though the difference is just fifty cents.

Percentage decrease: a 30% off jacket

Same idea, flipped around:

A jacket listed at $89 rings up at $62.30. Was that really 30% off?

• Discount taken: 89 − 62.30 = $26.70
• Divide by the original price: 26.70 ÷ 89 = 0.30
• Times 100: exactly 30%. The tag was honest.

The key phrase on sale tags: what you pay is 100% minus the discount. At 30% off, you pay 70% of the original: 89 × 0.70 = $62.30. One multiplication, done.

Discounts — and running them in reverse

The sale version of the formula, worth memorizing as its own line:

A $120 coat at 25% off: 120 × (1 − 0.25) = 120 × 0.75 = $90.

Now the reverse, which trips up smart people: you paid $45 for shoes that were 60% off. What was the original price? Solve for the original by dividing by what you actually paid:

• You paid 100% − 60% = 40% of the original.
• Original = 45 ÷ 0.40 = $112.50

This “divide by what’s left” move is the most useful percentage trick in shopping. Works for markdowns, after-tax prices, anything.

Calculate it in 30 seconds with the tool

The formulas are worth knowing, but life is short:

4 mistakes that give you the wrong number

• Mixing up percentage points and percent. If a mortgage rate moves from 6.5% to 7%, that’s 0.5 percentage points — but a 7.7% relative increase (0.5 ÷ 6.5). Headlines often blur these on purpose. Know which one you’re reading.
• Stacking discounts by adding them. A 20% coupon plus an extra 10% off is not 30% off. On a $100 item: 100 → 80 → $72 — a 28% total discount. Discounts multiply, they don’t add. This is also how store “70% off” clearance ends: two 50% cuts get you to 75% off, never 100%.
• Dividing by the wrong base. A raise from $50k to $60k is a 20% increase — but the drop back from $60k to $50k is only a 16.7% decrease, because the base changed. The denominator is always the starting value of that move.
• Rounding before the final step. Round 10.77% to 11% early in a multi-step calculation and the error compounds. Keep two decimals until the end, then round the answer.

Percentages get expensive when they compound: loan interest is the most expensive percentage you’ll ever meet. Our EMI guide works through exactly what a few percentage points cost you on a car loan and a mortgage.