Free Percentage Calculator
Calculate percentages with step-by-step explanations. Choose Learn Mode for interactive quizzes or Quick Mode for instant answers. Perfect for homework, exams, shopping discounts, tips, and more.
Step-by-step learning with explanations
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Find Percentage
What is X% of Y?
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What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning “by the hundred”. Percentages are everywhere in everyday life — from exam scores and shopping discounts to interest rates and statistics.
The Basics
25% means 25 out of 100, or 25/100, or 0.25 as a decimal. To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100.
Why Percentages Matter
Percentages let you compare quantities on a common scale. “80 out of 120” is harder to compare with “45 out of 60” — but 66.7% vs 75% is immediately clear.
Common Values
50% = half, 25% = quarter, 10% = tenth, 33.3% = third, 75% = three-quarters. Memorizing these makes mental math much faster.
Calculator Features
Everything you need for percentage calculations, from simple “what is X% of Y?” to reverse percentages and step-by-step learning.
6 Calculation Types
Find percentage of a number, what percentage X is of Y, percentage change, increase/decrease by percentage, and reverse percentage — all in one tool.
Gamified Learn Mode
Interactive step-by-step quizzes that break each problem into multiple choice questions. Practice like a game — perfect for exam practice.
Step-by-Step Workings
Every calculation shows detailed workings with LaTeX-rendered formulas, explanations at each step, and the final boxed answer.
Reference Sidebar
Built-in formula reference, fraction/decimal/percentage conversion table, mental math shortcuts, and real-world application examples.
History & Sharing
Calculation history persists across sessions (saved locally). Copy questions, answers, or share links with one click.
Example Problems
Pre-loaded examples for each calculation type. Click any example to instantly load it and see how the calculator works.
Percentage Formulas Quick Reference
The six core percentage formulas you need to know. Each formula is used by a different mode in the calculator above.
X% of Y
(X ÷ 100) × Y
Y × (X/100)
Example: 15% of 200 = 0.15 × 200 = 30
X is what % of Y?
(X ÷ Y) × 100
(Part ÷ Whole) × 100
Example: 30 is what % of 200? = 15%
Percentage Change
((New − Old) ÷ Old) × 100
Change ÷ Original × 100
Example: 80 → 100 = +25% increase
Increase by X%
Value × (1 + X/100)
Multiplier = 1 + X/100
Example: 100 + 20% = 100 × 1.20 = 120
Decrease by X%
Value × (1 − X/100)
Multiplier = 1 − X/100
Example: 100 − 25% = 100 × 0.75 = 75
Reverse Percentage
Result ÷ (X/100)
Result ÷ Multiplier
Example: 30 is 15% of what? = 200
Fraction, Decimal & Percentage Table
Key equivalents you should memorize. These come up constantly in AP, SAT, and everyday math.
| Fraction | Decimal | Percentage | Quick Trick |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half — divide by 2 |
| 1/3 | 0.333... | 33.3% | Third — divide by 3 |
| 1/4 | 0.25 | 25% | Quarter — divide by 4 |
| 1/5 | 0.2 | 20% | Fifth — divide by 5 |
| 1/8 | 0.125 | 12.5% | Eighth — half of a quarter |
| 1/10 | 0.1 | 10% | Tenth — divide by 10 |
| 2/3 | 0.666... | 66.7% | Two thirds |
| 3/4 | 0.75 | 75% | Three quarters — ÷4, ×3 |
| 4/5 | 0.8 | 80% | Four fifths — ÷5, ×4 |
| 7/8 | 0.875 | 87.5% | 100% − 12.5% |
Fraction → Percentage
Divide the fraction, then multiply by 100
3/4 = 0.75 × 100 = 75%
Percentage → Decimal
Divide by 100 (move decimal 2 left)
45% = 45 ÷ 100 = 0.45
Decimal → Percentage
Multiply by 100 (move decimal 2 right)
0.35 = 0.35 × 100 = 35%
Percentage Change Explained
Percentage change is one of the most tested topics in high school math. Here are the key concepts and common pitfalls.
The Formula
% Change = ((New − Old) ÷ Old) × 100
Always divide by the original (old) value. Positive result = increase, negative = decrease.
The Multiplier Method
20% increase → multiply by 1.20
15% decrease → multiply by 0.85
7.5% increase → multiply by 1.075
33% decrease → multiply by 0.67
Common Mistake
A 50% increase followed by a 50% decrease does NOT return to the original value!
100 → +50% → 150 → −50% → 75 (not 100)
The decrease uses the new (larger) value as its base.
Successive Changes
For multiple percentage changes, multiply the multipliers together:
+10% then +20% = 1.10 × 1.20 = 1.32 (32% total increase)
Not 30% — the second increase applies to the already-increased value.
Real-World Percentage Applications
Percentages are used everywhere. Here are the most common real-world scenarios.
Shopping Discounts
30% off $80: $80 × 0.70 = $56. Use "Decrease by %" in the calculator.
Use: Decrease by %Sales Tax Calculations
Add 8% sales tax: price × 1.08. Remove tax (reverse): price ÷ 1.08. $108 inc. tax = $100 before tax.
Use: Increase / Reverse %Restaurant Tips
15% tip on $45 bill: $45 × 0.15 = $6.75. Total = $51.75. Split between 2: $25.88 each.
Use: Find %Salary & Pay Raises
3% pay raise on $28,000: $28,000 × 1.03 = $28,840. That is an extra $840 per year.
Use: Increase by %Exam Scores
72 out of 90: (72 ÷ 90) × 100 = 80%. Grade boundaries are set as percentages.
Use: What % of?Price Comparisons
Was $250, now $199. Change: ((199−250) ÷ 250) × 100 = −20.4% decrease.
Use: % ChangeMental Math Percentage Shortcuts
These shortcuts help you estimate percentages quickly without a calculator — useful for exams and everyday life.
Quick Division Tricks
The Flip Trick
X% of Y = Y% of X
8% of 25 = 25% of 8 = 2
4% of 75 = 75% of 4 = 3
If one way is hard, flip it around! This works because multiplication is commutative.
Build Up Method
Break complex percentages into simple ones and add/subtract:
15% = 10% + 5%
35% = 25% + 10%
17.5% = 10% + 5% + 2.5%
90% = 100% − 10%
AP & Exam Tips for Percentages
Percentage questions appear on every AP, SAT, and ACT exam. Here are the key topics and how to tackle them.
Non-Calculator Section
- •Use the build-up method: find 10%, 5%, 1% then combine
- •Memorize key fraction ↔ percentage equivalents
- •Use the flip trick: X% of Y = Y% of X
- •Show your working — method marks are available even if the answer is wrong
Calculator Section
- •Use the multiplier method for speed: ×1.15 for 15% increase
- •For reverse percentage: divide by the multiplier, not subtract
- •Successive changes: multiply multipliers together
- •Double-check: does your answer make sense? Increase should be bigger, decrease smaller
Common Exam Questions
- •"Find the original price after a 20% discount" = reverse percentage
- •"Which store offers the better deal?" = calculate both and compare
- •"After 2 years of 5% compound interest" = ×1.05²
- •"Tax is added then removed — is it the same?" = no, explain why
Scoring Guide Tips
- •Always show the multiplier/decimal conversion step
- •State whether a change is an increase or decrease
- •Round only at the final step, not intermediate steps
- •Include units ($, %, etc.) in your final answer
Frequently Asked Questions
How do I find a percentage of a number?
Divide the percentage by 100 to get a decimal, then multiply by the number. For example, 15% of 200: divide 15 by 100 to get 0.15, then 0.15 × 200 = 30.
How do I calculate percentage change?
Subtract the old value from the new, divide by the old value, multiply by 100. Always divide by the ORIGINAL value. Positive = increase, negative = decrease.
What is reverse percentage?
Finding the original number when you know the result and the percentage. If the sale price is $60 after a 20% discount, divide by 0.80 to find the original price: $75.
How do I calculate a discount?
Use "Decrease by %" — multiply the price by (1 − discount/100). For 30% off $80: $80 × 0.70 = $56. The multiplier for 30% off is 0.70.
How do I add or remove sales tax?
Add tax: multiply by (1 + rate/100). Remove tax: divide by (1 + rate/100). For example, $108 with 8% tax ÷ 1.08 = $100 before tax.
Why does 50% up then 50% down not equal the original?
Because the decrease applies to the larger (increased) value. 100 + 50% = 150. Then 150 − 50% = 75, not 100. The base changes between operations.
What is the multiplier method?
Converting percentage changes into a single multiplication. 20% increase → ×1.20, 15% decrease → ×0.85. For successive changes, multiply multipliers: ×1.10 × ×1.20 = ×1.32.
How do I convert fractions to percentages?
Divide the numerator by the denominator, then multiply by 100. For example, 3/8 = 0.375 = 37.5%. Or multiply the fraction by 100: (3/8) × 100 = 37.5%.
What mental math shortcuts work for percentages?
10% = ÷10, 5% = half of 10%, 1% = ÷100, 25% = ÷4. Combine: 15% = 10% + 5%. The flip trick: X% of Y = Y% of X (e.g., 8% of 25 = 25% of 8 = 2).
Can I use this for compound percentage changes?
For compound changes (like compound interest), use the increase/decrease calculator multiple times, or calculate the compound multiplier: e.g., 5% for 3 years = 1.05³ = 1.1576 (15.76% total).
Is this calculator suitable for AP and SAT practice?
Yes! It covers all AP and SAT percentage topics including the multiplier method, reverse percentages, and successive changes. Learn Mode provides gamified step-by-step practice with multiple choice questions.
What if I get a negative percentage?
A negative percentage change means a decrease. For example, −25% means the value went down by a quarter. In "percentage change" mode, negative indicates the new value is smaller than the old.
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