Percentage Calculator
Calculate percentages, percentage change, reverse percentages, and part-to-whole ratios using decimals or fraction inputs like 3/4 and 1.5/2.5.
Last updated: 2026-03-28
Choose a calculation mode
Pick the percentage question you need to solve.
Percentage calculator
Enter your values
Fill in the fields for the selected mode. Required fields are marked with an asterisk. Decimals and fractions like 3/4 or 1.5/2.5 are accepted.
Result
50.00
25% of 200 equals 50.
Calculation History (0)
Examples you can apply
Tap an example to prefill the calculator with realistic values.
Percent of a Number
Restaurant Tip
20% of $85
Standard tip calculation for good service.
Result: $17.00
Discount Savings
15% of $250
Estimate how much you save during a sale.
Result: $37.50
Sales Tax
8.25% of $1,500
Calculate tax on a larger purchase.
Result: $123.75
Half of a Recipe Batch
50% of 1.5/2.5
Use a fraction expression as the base number when scaling ingredients or split quantities.
Result: 0.30
Percentage Change
Investment Return
$100 to $135
Track growth on a stock investment over time.
Result: +35% increase
Weight Loss
180 lbs to 165 lbs
Measure progress toward a health goal.
Result: -8.33% decrease
Price Increase
$3.50 to $4.20
Understand inflation on everyday items.
Result: +20% increase
Fractional Yield Change
1.5/2.5 to 3/4
Compare two ratio values even when both are entered as fractions.
Result: +25% increase
Reverse Percentage
Test Score
45 is 90% of what?
Find the full score from a percentage grade.
Result: 50
Original Price
$80 is 80% of what?
Determine the pre-discount price of an item.
Result: $100.00
Commission Total
$500 is 5% of what?
Back into a total sale from a commission payout.
Result: $10,000.00
Part to Percentage
Fractional Share of a Whole
1.5/2.5 out of 3/4
Find what percent one ratio is of another using fraction-style input in both fields.
Result: 80.00%
Quarter Completed
3/8 out of 1/2
Translate a part and whole into a percentage without doing the fraction conversion yourself.
Result: 75.00%
How Percentage Calculations Work
Percentages express a number as a fraction of 100. The word "percent" literally means "per hundred." Percentage calculations appear everywhere in daily life — from calculating tips and discounts to understanding tax rates, investment returns, and test scores. Mastering four common operations, plus knowing how to move between decimals and fractions, lets you solve virtually any percentage problem.
Finding a Percentage of a Number
To find X% of Y, multiply Y by X/100. For example, 20% of $85 is $85 × 0.20 = $17. This is the most common percentage operation — used for tips, sales tax, discounts, and commission calculations. The key is converting the percentage to a decimal first by dividing by 100.
Calculating Percentage Change
Percentage change measures how much a value increased or decreased relative to its starting point. The formula is ((New - Original) / |Original|) × 100. Going from $80 to $100 is a 25% increase. Going from $100 to $80 is a 20% decrease. Notice these are not the same percentage — because each calculation uses a different base value. This asymmetry is important in finance: a 50% portfolio loss requires a 100% gain to recover.
Reverse Percentage (Finding the Base)
Sometimes you know the result and the percentage, but need to find the original number. If an item costs $60 after a 25% discount, the sale price represents 75% of the original. Divide $60 by 0.75 to get $80. This reverse calculation is useful for back-calculating prices, determining test totals from scores, and finding base values from commission payouts.
Finding What Percent One Value Is of Another
When you already know the part and the whole, divide the part by the whole and multiply by 100. If you completed 3/8 of a project out of a 1/2 target, the calculation is (0.375 / 0.5) × 100 = 75%. This mode is useful for grades, completion tracking, and comparing one ratio against another.
Key tips
- Always identify which number is the base (the 100% reference point).
- Percentage increase and decrease are not symmetric — a 50% increase followed by a 50% decrease does not return to the original value.
- Percentages above 100% mean the value exceeds the base.
- Fraction inputs like 3/4 or 1.5/2.5 are converted to decimals before calculation.
- Percentage change from zero is undefined because it requires division by zero. Report the absolute change instead.
Percentage calculator FAQs
Answers to common questions about percentage math.
How do I calculate what percentage one number is of another?
To find what percentage X is of Y, divide X by Y and multiply by 100. For example, if you scored 45 out of 50 on a test: (45 / 50) x 100 = 90%. Use the Part to Percent mode when you already know the part and the whole and want the percentage directly.
What is the formula for percentage change?
Percentage change = ((New Value - Original Value) / |Original Value|) x 100. The absolute value in the denominator ensures the direction of change is shown in the result sign. A positive result means increase; negative means decrease. From $100 to $75 is -25%, indicating a 25% decrease.
Can I calculate percentage change from zero?
No, percentage change from zero is mathematically undefined because it requires division by zero. When your starting value is zero, percentage change has no meaning. In real-world contexts, you might note this as infinite growth or simply report the absolute change instead. Our calculator will display an explanatory message rather than an error.
How do I reverse-calculate an original price from a sale price?
If an item is discounted by 20%, the sale price represents 80% of the original. Use reverse percentage: divide the sale price by 0.80 (or 80 / 100). For a $60 item after 25% off: $60 / 0.75 = $80 original price. The key is recognizing that the sale price equals (100% - discount%) of the original.
Can I enter fractions like 3/4 or 1.5/2.5?
Yes. Every numeric field now accepts regular decimals and fraction expressions. That includes standard fractions like 3/4 and decimal fractions like 1.5/2.5. The calculator converts those inputs to decimals before running the formula.
What does the Part to Percent mode do?
Part to Percent answers the direct numerator/denominator question: 'What percent is this part of that whole?' Enter the part in the numerator field, the whole in the denominator field, and the calculator returns the percentage, the decimal equivalent, and the simplified fraction. It is especially useful for grades, completion tracking, and comparing two ratio values.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. For example, 3/8 = 0.375 = 37.5%. Use the Part to Percent mode to get the percentage, decimal, and simplified fraction all at once. Common conversions: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 1/8 = 12.5%.
Why does a 50% increase followed by 50% decrease not equal the original?
Percentage changes are relative to different bases. Starting with 100: a 50% increase gives 150 (100 x 1.5). Then a 50% decrease from 150 gives 75 (150 x 0.5), not 100. The decrease is calculated from the larger number. This asymmetry is crucial in finance; a 50% portfolio loss requires a 100% gain to recover.
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Disclaimer
This calculator is for educational and general informational purposes only. Results are estimates based on the formulas and inputs provided. For financial decisions, consult a qualified professional. Calc Hub is not responsible for errors or decisions made based on calculator results.
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