Percentage Calculator
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Solve 6 types of percentage problems instantly: find a percentage, percentage change, percentage of total, increase/decrease, and reverse percentage.
% Percentage Calculator
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How to Use the Percentage Calculator
Select the calculation type
Choose from the six types: percentage of a number (what is X% of Y?), percentage change between two values, what percentage one number is of another, original value from a percentage, percentage increase/decrease, and reverse percentage.
Enter your values
Input the relevant numbers for your chosen calculation type. Labels update to match the selected mode so you always know which value goes where.
Read the result and formula
The result shows instantly alongside the formula used. This confirms which calculation was performed and lets you verify the logic manually.
Use the percentage change type for price comparisons
For comparing sale prices, investment returns, or year-over-year metrics, the percentage change calculation (new − old ÷ old × 100) is the most commonly needed type.
Percentage Formulas — All Types Explained
Percentages appear everywhere in everyday life: discounts, tax rates, interest rates, grade calculations, statistics, and financial analysis. Here are the core formulas:
📐 Core Percentage Formulas
How to Calculate a Percentage — 3 Core Methods
Percentage calculations fall into three main categories that cover almost every real-world situation. Understanding each formula makes mental math faster and helps you verify calculator results.
Method 1: What is X% of Y?
Formula: Result = (X ÷ 100) × Y
Example: What is 15% of $85 (restaurant tip)? = (15 ÷ 100) × 85 = $12.75
Method 2: What percentage is X of Y?
Formula: Percentage = (X ÷ Y) × 100
Example: You scored 43 out of 60 on a test. What percentage? = (43 ÷ 60) × 100 = 71.7%
Method 3: Percentage Change (Increase or Decrease)
Formula: % Change = ((New Value − Old Value) ÷ Old Value) × 100
Example: Price went from $80 to $92. Percentage increase? = ((92 − 80) ÷ 80) × 100 = 15% increase
Percentage Increase vs Percentage Point Increase
These are often confused. If interest rates go from 2% to 3%, that's a 1 percentage point increase but a 50% increase in the rate itself. Percentage points describe absolute change in a percentage value; percentages describe relative change. This distinction matters enormously in finance, statistics, and politics.
Quick Mental Percentage Tricks
- 10%: Move the decimal point one place left. 10% of $347 = $34.70
- 5%: Half of 10%. 5% of $347 = $17.35
- 20%: Double the 10% figure. 20% of $347 = $69.40
- 15%: Add 10% + 5%. 15% of $347 = $34.70 + $17.35 = $52.05
- 25%: Divide by 4. 25% of $80 = $20
- 1%: Move decimal two places left. 1% of $3,400 = $34
Common Real-World Percentage Calculations
| Situation | Calculation | Example |
|---|---|---|
| Sales discount | Original × (1 − discount%) | $120 × 0.75 = $90 (25% off) |
| Tax added | Price × (1 + tax%) | $50 × 1.08 = $54 (8% tax) |
| Tip calculation | Bill × tip% | $85 × 0.20 = $17 tip |
| Investment return | ((End − Start) ÷ Start) × 100 | ($12,000 − $10,000) ÷ $10,000 = 20% |
| Grade score | (Correct ÷ Total) × 100 | (38 ÷ 50) × 100 = 76% |
How to Calculate a Percentage Increase and Decrease by Hand: Worked Example
A $1,200 salary is raised by 8%, then the following year reduced by 8% due to a pay cut. Intuitively, this might seem to return to the original amount — it doesn't.
Step 1 — apply the 8% raise. $1,200 × 1.08 = $1,296.00.
Step 2 — apply the 8% cut to the new, higher amount. $1,296.00 × 0.92 = $1,192.32.
The final amount is $7.68 lower than the original $1,200 — a net change of −0.64%, not 0%. This happens because the 8% cut is calculated on the larger post-raise amount, so it removes more dollars than the 8% raise added. Equal-percentage increases and decreases never fully cancel out except in the trivial case of 0%.
What's the difference between a "percentage point" and a "percent" change?
If an interest rate moves from 5% to 7%, that's a 2 percentage point increase — but expressed as a relative percentage change, it's a 40% increase (2 ÷ 5 = 0.40). Financial and political reporting often uses these two phrasings interchangeably in casual language, but they describe very different magnitudes — mixing them up is one of the most common sources of misread statistics in news coverage.
Three Ways to Calculate Any Percentage Problem
Method 1 — What is X% of Y?
Multiply: X% of Y = (X ÷ 100) × Y. What is 15% of $80? (15 ÷ 100) × 80 = $12. This is the standard "tip calculation" and "tax calculation" form.
Method 2 — What percentage is X of Y?
Divide and multiply by 100: (X ÷ Y) × 100. If you scored 42 out of 50 on a test: (42 ÷ 50) × 100 = 84%. This is the standard "grade" or "completion rate" form.
Method 3 — Percentage change between two values
(New − Old) ÷ Old × 100. A stock moving from $40 to $46: (46 − 40) ÷ 40 × 100 = +15%. Note this formula always divides by the original value, not the new one — dividing by the new value instead is a common calculation error that understates increases and overstates decreases.
What are some quick mental-math shortcuts for common percentages?
10% of any number is found by moving the decimal point one place left (10% of $85 = $8.50); 5% is half of that ($4.25); 1% moves the decimal two places left ($0.85). Combining these — 15% = 10% + 5% — lets you calculate a restaurant tip on $85 as $8.50 + $4.25 = $12.75 without a calculator.
Frequently Asked Questions
Sources & Methodology
Calculations are based on the most current publicly available data from authoritative government and industry sources: