Percentage Calculator

Percentage Calculator: Your Complete Guide to Percentage Calculations

Percentages are everywhere in daily life—from discounts and tips to grades and statistics. Yet percentage calculations often trip people up, especially when the question is phrased differently than expected. Our comprehensive percentage calculator handles five common calculation types with step-by-step solutions, making it both a calculation tool and a learning resource. Whether you need to find what 25% of 80 is, what percentage 20 is of 80, or calculate the percentage change between two values, this tool provides instant, accurate answers.

The step-by-step breakdown is particularly valuable for students learning percentage concepts or anyone wanting to understand the math behind the result—not just get an answer. Each calculation shows the formula applied and walks through the arithmetic, building confidence for future calculations. For related financial calculations, explore our Discount Calculator, Margin Calculator, and Markup Calculator.

The Five Types of Percentage Problems

1. What is X% of Y? This is the most common percentage question. To find 25% of 200, convert the percentage to a decimal (25% = 0.25) and multiply: 0.25 × 200 = 50. This calculation is used for discounts ("What's 20% off $80?"), tips, taxes, and countless other daily situations.

2. X is what percent of Y? This finds what percentage one number represents of another. If you scored 45 out of 60, what's your percentage? Divide the part by the whole and multiply by 100: (45 ÷ 60) × 100 = 75%. Used for grades, statistics, and comparing quantities.

3. X is Y% of what? This reverse calculation finds the original whole when you know a part and its percentage. If $30 represents 15% of your income, what's your income? Divide the part by the percentage: 30 ÷ 0.15 = $200. Useful for reconstructing original values from partial information.

4. Percentage change measures how much something increased or decreased from an original value: ((New - Old) ÷ Old) × 100. If prices rose from $80 to $100, that's ((100 - 80) ÷ 80) × 100 = 25% increase. Essential for financial analysis, growth tracking, and comparing periods.

5. Percentage difference compares two values without treating either as "original": |A - B| ÷ ((A + B) ÷ 2) × 100. Unlike percentage change, this is symmetric—the difference between 80 and 100 is the same regardless of which you list first. Used when comparing alternatives without a clear baseline. Check savings with our Savings Calculator.

Common Percentage Mistakes and How to Avoid Them

Mistake: Adding/subtracting percentages incorrectly. A 10% increase followed by a 10% decrease doesn't return you to the original—it leaves you 1% below. If $100 increases 10% to $110, then decreases 10%, you get $99. Percentages compound multiplicatively, not additively.

Mistake: Confusing percentage change with percentage points. If interest rates rise from 2% to 3%, that's a 1 percentage point increase but a 50% relative increase. Both are valid ways to describe the change, but they're very different numbers. Always clarify which measure is being used.

Mistake: Using the wrong base. "50% more than X" means 1.5X, not 0.5X. "50% of X" means 0.5X. Small wording differences completely change the calculation. Read problems carefully to identify what's being asked.

Quick Mental Math Tricks for Percentages

Finding 10%: Just move the decimal point one place left. 10% of 85 = 8.5. This is your building block for many other percentages.

Finding 5%: Find 10% and halve it. 5% of 85 = 4.25 (half of 8.5).

Finding 15%: Add 10% + 5%. For 15% of 85: 8.5 + 4.25 = 12.75.

Finding 20%: Double 10%. 20% of 85 = 17.

Finding 25%: Divide by 4. 25% of 85 = 21.25.

Switching numbers: X% of Y = Y% of X. So 8% of 50 = 50% of 8 = 4. Use whichever is easier to calculate! For tax calculations, see our GST Calculator and VAT Calculator.

Frequently Asked Questions About Percentages

How do I calculate percentage increase?

((New Value - Original Value) ÷ Original Value) × 100. If salary increased from $50,000 to $55,000: ((55,000 - 50,000) ÷ 50,000) × 100 = 10% increase.

How do I calculate percentage decrease?

Same formula—the result will be negative. If price dropped from $100 to $75: ((75 - 100) ÷ 100) × 100 = -25%, or a 25% decrease.

What's the difference between percent and percentage point?

Percentage points measure the arithmetic difference between two percentages. From 20% to 25% is 5 percentage points. "Percent" would describe the relative change: (25-20)/20 × 100 = 25% increase. These are different numbers describing the same change differently. Calculate tips with our Tip Calculator.

How do I reverse a percentage?

To find the original before a percentage increase: divide by (1 + rate). If something is $120 after 20% increase: $120 ÷ 1.20 = $100 original. For percentage decrease: divide by (1 - rate).