percentage calculator formula

How the percentage calculator formula works

Percentages are one of the most useful tools in everyday math. Whether you are calculating discounts, exam scores, tax, tips, investment returns, or business growth, the same small set of formulas keeps showing up.

The word percent literally means “per hundred.” So 35% means 35 out of 100, which is the same as 0.35 in decimal form. Most percentage problems become easy once you convert that percent into a decimal and apply the right formula.

Core percentage formulas you should know

1) Find a percentage of a number

Formula: Percentage Value = (Percent ÷ 100) × Number

• Example: 20% of 250 = (20 ÷ 100) × 250 = 50
• Use this for sales discounts, tax amounts, and tip calculations.

2) Find what percent one number is of another

Formula: Percent = (Part ÷ Whole) × 100

• Example: 18 is what percent of 24? (18 ÷ 24) × 100 = 75%
• Use this for scores, completion rates, and conversion rates.

3) Find percentage increase or decrease

Formula: Change % = ((New − Old) ÷ Old) × 100

• Example: Price from 80 to 100 → ((100 − 80) ÷ 80) × 100 = 25% increase
• Example: Price from 100 to 80 → ((80 − 100) ÷ 100) × 100 = -20% (20% decrease)

4) Add or subtract a percentage from a value

To add a percentage: New Value = Base × (1 + p/100)
To subtract a percentage: New Value = Base × (1 - p/100)

• Add 8% tax to 50: 50 × 1.08 = 54
• Subtract 30% discount from 90: 90 × 0.70 = 63

Step-by-step example set

Example A: Discount shopping

A jacket costs $120 and is on a 25% discount.

• Discount amount = 25% of 120 = 30
• Final price = 120 − 30 = 90

Example B: Grade calculation

You scored 42 out of 50 on a test.

• Percent score = (42 ÷ 50) × 100 = 84%

Example C: Salary growth

Salary increased from 48,000 to 52,800.

• Change = 52,800 − 48,000 = 4,800
• Growth % = (4,800 ÷ 48,000) × 100 = 10%

Common percentage mistakes to avoid

• Dividing by the wrong base: In “A is what percent of B,” divide A by B, not B by A.
• Forgetting to multiply by 100: The decimal 0.18 is 18%, not 0.18%.
• Mixing up increase and decrease: A negative result means decrease.
• Applying percentages in the wrong order: Two 10% changes do not always cancel each other.

Quick cheat sheet

• X% of Y: (X/100) × Y
• A is what % of B: (A/B) × 100
• % change: ((New − Old)/Old) × 100
• After adding p%: Base × (1 + p/100)
• After subtracting p%: Base × (1 − p/100)

When to use a percentage calculator

Mental math is great for rough estimates, but a calculator helps when precision matters. Use one for budgeting, business reports, tax planning, exam calculations, investment analysis, and price comparisons. A quick percentage calculator formula tool saves time and reduces mistakes.

If you want speed and confidence, memorize the four core formulas above and use the calculator section at the top of this page whenever values are large or decimal-heavy.