Percentages are the language of everyday numbers: sale discounts, restaurant tips, sales tax, pay raises, investment returns. Most people remember the formulas but freeze when the numbers are real — especially with stacked discounts or working backward to an original price. This guide covers every percentage scenario with worked examples in dollars.

How to Use the Percentage Calculator

1. Open the Percentage Calculator tool above.
2. Pick the mode that matches your question: X% of Y, X is what percent of Y, or percentage increase / decrease.
3. Enter the two numbers and click Calculate — the answer appears instantly.

The 3 Core Formulas

You want	Formula	Example
X% of Y	(X ÷ 100) × Y	20% of $150 = $30
X as a % of Y	(X ÷ Y) × 100%	$30 of $120 = 25%
Percentage change	((New − Old) ÷ Old) × 100%	$100 → $150 = +50%

Case 1: Finding X% of a Number

The most common case — discounts, tax, tips, commission.

Discount: a $350 jacket at 30% off. Discount = 0.30 × 350 = $105, so you pay $245.

Tip: an $80 bill with an 18% tip. Tip = 0.18 × 80 = $14.40; total $94.40.

Sales tax: a $220 purchase with 8% tax. Tax = 0.08 × 220 = $17.60; total $237.60.

Case 2: What Percent Is X of Y?

The reverse: you know the numbers and want the percentage.

Test score: 27 correct out of 36 questions → (27 ÷ 36) × 100% = 75%.

Sales target: $37,500 achieved out of a $50,000 target → 75%.

Case 3: Percentage Increase and Decrease

Formula: ((New − Old) ÷ Old) × 100%. The divisor is always the old value — getting this wrong is the single most common percentage mistake.

Pay raise: $60,000 → $66,000 = +10%.

Price drop: $80 → $60 = −25%.

Reverse Percentage: Finding the Original Price

A case rarely explained well: you know the price after the discount and want the original. Formula: Original = Final ÷ (1 − Discount/100).

Example: after a 20% discount you paid $400. Original = 400 ÷ 0.8 = $500. Check: 20% of $500 = $100; $500 − $100 = $400 ✓.

Stacked Discounts Don’t Add Up

A classic trap: 50% off plus 20% off is not 70% off. The second discount applies to the already-reduced price.

Example: a $200 item at 50% then 20% off → $200 × 0.5 = $100, then $100 × 0.8 = $80. The real total discount is 60%, not 70%. Quick formula: final price = original × (1 − d1) × (1 − d2).

Mental Math: The 10% Trick

10% of anything is just the decimal point moved one place left. Build everything else from there:

• 10% of $250 = $25
• 5% = half of 10% → $12.50
• 15% = 10% + 5% = $25 + $12.50 = $37.50
• 20% = double 10% = $50

This handles most tip and discount math in seconds while you’re shopping.

Margin vs. Markup: Don’t Mix Them Up

	Formula	Example (cost $80, price $100)
Markup	(Profit ÷ Cost) × 100%	25%
Margin	(Profit ÷ Price) × 100%	20%

Markup asks “how much did I raise the cost”; margin asks “what share of the price is profit”. Financial reports use margin.

Common Percentage Mistakes

• Wrong divisor: percent change always divides by the old value, never the new one.
• Adding stacked discounts — always multiply step by step instead.
• Forgetting the decimal: 20% = 0.20, not 20. This mistake throws results off 100-fold.
• Up 50% then down 50% isn’t break-even: $100 → $150 → $75. Recovering from a 50% loss actually requires a 100% gain.

Percentage Calculator FAQs

What is 15% of 200?
0.15 × 200 = 30.

How do I calculate percentages on a phone calculator without a % key?
Convert to a decimal first: 25% = 0.25, then multiply normally (80 × 0.25 = 20).

What is the total of a 30% + 20% discount?
Not 50%! Final price = 1 × 0.7 × 0.8 = 0.56, so the total discount is 44%.

What’s the difference between a discount and cashback?
A discount cuts the price upfront. Cashback returns part of your money after you pay full price — usually as points or credit, not a price cut.

How do I find the original price from a sale price?
Divide what you paid by (1 − discount). Paid $170 after 15% off → 170 ÷ 0.85 = $200.

Quick Reference: Percent, Decimal, Fraction

Converting between forms is a daily need:

• Percent to decimal: divide by 100 — 25% = 0.25
• Decimal to percent: multiply by 100 — 0.25 = 25%
• Common pairs to memorize: 50% = 1/2, 25% = 1/4, 75% = 3/4, 20% = 1/5, 10% = 1/10, 12.5% = 1/8

Knowing 12.5% = 1/8 makes mental math much faster: 12.5% of $800 is simply $800 ÷ 8 = $100.

More math tools: Online Calculator and Unit Converter.