Percentage Calculator Guide: Increase, Decrease & Tip Math Made Simple

Almost every percentage problem reduces to one of three patterns. Once you spot which pattern you're looking at, the math takes ten seconds.

The Three Core Patterns

1. What is X% of Y?

Multiply: (X ÷ 100) × Y. What is 18% of $84? → 0.18 × 84 = $15.12.

2. X is what percent of Y?

Divide and multiply by 100: (X ÷ Y) × 100. 32 out of 80 → 32 ÷ 80 = 0.4 → 40%.

3. Percent change from old to new

((new − old) ÷ old) × 100. From $200 to $250 → (50 ÷ 200) × 100 = +25%. From $80 to $60 → (−20 ÷ 80) × 100 = −25%.

Sales Tax & Tips

To add a percentage onto a price, multiply by (1 + rate). Adding 8.5% tax to $40 → 40 × 1.085 = $43.40. To strip tax from a tax-inclusive price, divide by (1 + rate): $43.40 ÷ 1.085 = $40.00.

For tips: 10% is one decimal place left; double it for 20%; halve it again for 5%. Combine for any tip you want. $54 check → 10% = $5.40 → 20% = $10.80 → 15% = $8.10.

Discounts the Right Way

A 30% discount means you pay 70% of the original. Just multiply by 0.70 — don't calculate the discount and subtract; it's one less step. $120 jacket at 30% off → 120 × 0.7 = $84.

Stacked Percentages Don't Add

A 20% raise followed by a 20% pay cut does not return you to your starting salary. $50,000 × 1.20 = $60,000 → × 0.80 = $48,000. You're $2,000 worse off because the cut applied to a bigger number. Always multiply sequential changes, never add them.

Frequently Asked Questions