Percentage Calculator - Percent Change, Discounts, Ratios

Try These Examples

20% of 500

100

30 is what % of 120?

25%

1,000 + 15%

1,150

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Result

Formula

Step-by-Step

Useful Info

Quick Formula Reference

Find X% of Y

(X ÷ 100) × Y

Example: 25% of 200 = (25 ÷ 100) × 200 = 50

X is what % of Y?

(X ÷ Y) × 100

Example: 50 is what % of 200? = (50 ÷ 200) × 100 = 25%

Percentage Change

((New - Old) ÷ Old) × 100

Example: 100 → 150 = ((150 - 100) ÷ 100) × 100 = 50%

Apply Percentage

Original × (1 ± X/100)

Example: 100 + 20% = 100 × 1.20 = 120

Percentage Difference

|A - B| ÷ ((A + B) ÷ 2) × 100

Example: 100 vs 120 = 20 ÷ 110 × 100 = 18.18%

Reverse Percentage

Final ÷ (1 ± Rate/100)

Example: 120 after +20% = 120 ÷ 1.20 = 100

What Can You Calculate?

Restaurant Tips

Figure out 15%, 18%, or 20% tips on your bill in seconds

Sale Discounts

See the actual price after a 30% off sale or any discount

Test Grades

Convert correct answers to a percentage (42 out of 50 = 84%)

Price Changes

Track how much prices went up or down over time

Sales Tax

Add 8% sales tax to find your total purchase price

Investment Returns

Calculate gains and losses as percentages

Don't Make These Mistakes

Percentage vs Percentage Points

If interest rates go from 5% to 8%, that's a 3 percentage point increase, not a 3% increase. The actual percentage increase is 60% (because (8-5)/5 = 0.6 = 60%). News reports mess this up constantly.

You Can't Just Reverse a Percentage

Start with $100. Increase it 50% and you get $150. Now decrease $150 by 50% and you're at $75, not back to $100. Why? The 50% decrease applies to $150, not the original $100. Percentages use different bases, so they don't reverse symmetrically.

Adding Discounts Doesn't Work That Way

A 20% discount plus a 10% discount is NOT 30% off. They multiply: $100 × 0.80 × 0.90 = $72, which is only 28% off. Each discount applies to the current price, not the original.

Use Percentage Difference for Comparisons

When comparing two values without an obvious "before" and "after," use percentage difference instead of percentage change. It's symmetric, so comparing 100 to 120 gives the same result as comparing 120 to 100 (18.18%).

How Do Percentages Actually Work?

Percentage means "per hundred." It comes from the Latin "per centum." When you see 25%, you're looking at 25 per 100, or 25/100, or 0.25. They all mean exactly the same thing: one quarter.

Percentages normalize everything to a common scale. A raw score of 45 out of 60 is harder to judge than 75%, which immediately shows the result on a 100-point scale.

Converting Percentages to Decimals

Move the decimal point two places left. The same rule works for small percentages, whole percentages, and percentages over 100%.

25% becomes 0.25. Just divide by 100 in your head by moving that decimal. 8% becomes 0.08 (add a zero). 150% becomes 1.50. Once you've got the decimal, you can actually use it in calculations. "What's 25% of 200?" becomes "What's 0.25 × 200?" which is 50.

Converting Decimals to Percentages

Reverse it. Move the decimal two places right and slap a % symbol on it. 0.25 is 25%. 0.5 is 50%. 1.5 is 150%. Simple.

Why Percentages Beat Fractions

Quick: which is better, saving 3/8 of your income or 2/5? Hard to tell. Now: which is better, saving 37.5% or 40%? Obvious.

Percentages put everything on the same scale (0 to 100), making instant comparisons possible. Your brain doesn't need to find common denominators or do fraction division. That's why stores advertise "30% off" instead of "3/10 off" and teachers give you 85% instead of 17/20.

Percentages Over 100%

Yes, this is allowed. 200% means twice the original. 150% means one and a half times. When you hear "sales increased 300%," that means they quadrupled (went to 400% of the original, which is 4× the original). Corporate earnings reports love talking this way, by the way. Makes small gains sound impressive.

Quick Mental Math Tricks

To find 10% of anything, move the decimal one place left. 10% of 450 is 45.

Want 1%? Move it two places left. 1% of 450 is 4.5.

Want 5%? Find 10% and cut it in half. 5% of 450 is 22.5.

A useful shortcut: 20% of 50 equals 50% of 20. Both equal 10 because percentages are commutative when multiplied.

Percentage Change: The Math That Trips Everyone Up

The formula is ((New - Old) / Old) × 100. New value minus old value, divided by the old value, times 100. This tells you how much something grew or shrank relative to where it started.

Your rent went from $1,000 to $1,200? That's ((1200 - 1000) / 1000) × 100 = 20% increase.

Positive result means it went up. Negative means it went down. Stock goes from $100 to $120? That's a 20% increase. Stock drops from $120 to $100? That's a 16.67% decrease. Notice those aren't the same number? A 20% increase followed by a 16.67% decrease gets you back to start. The percentages differ because they're calculated from different bases.

Percentage changes multiply; they do not add. Start with $100, increase it 20% to $120, then increase it another 10%. The second 10% applies to $120, not the original $100. The result is $120 × 1.10 = $132, so the actual total increase is 32%.

Working backwards? You know something costs $150 after a 25% increase. What did it cost before? Divide by (1 + rate): $150 / 1.25 = $120. After a 25% decrease? Divide by (1 - rate): $150 / 0.75 = $200.

Real Situations Where You'll Use This

For an $80 bill with an 18% tip, 10% is $8 and 20% is $16. Since 18% is close to 20%, the tip should be a little below $16.

Sale prices: Shirt is $50 with 30% off. Calculate the discount ($50 × 0.30 = $15 off, so $35 final) or multiply by what remains ($50 × 0.70 = $35). Same answer.

Test scores: Got 42 out of 50 right? (42 / 50) × 100 = 84%.

Comparing stores: Store A has a TV for $500 with 20% off ($400 final). Store B has it for $450 with 10% off ($405 final). Store A wins by $5.

Converting Between Percentages, Decimals, and Fractions

These are all the same thing, just written differently. You'll switch between them constantly.

Percentage to decimal? Divide by 100. Just move the decimal two places left. 25% becomes 0.25. 8% becomes 0.08. Done.

Decimal to percentage? Reverse it. Move the decimal two places right. 0.25 is 25%. 1.5 is 150%.

Percentage to fraction? Write it over 100, then simplify. 25% = 25/100 = 1/4.

Fraction to percentage? Divide top by bottom, multiply by 100. So 1/4 = 0.25 = 25%.

Memorize these. It'll save you time:

1/2 = 50%. 1/4 = 25%. 3/4 = 75%. 1/3 = 33.33%. 2/3 = 66.67%. 1/5 = 20%. 1/10 = 10%. 1/8 = 12.5%.

Common Questions

How do you calculate a percentage of a number?

Convert the percentage to a decimal by dividing by 100, then multiply by the number. For example, 25% of 200 is 0.25 x 200 = 50.

How is percentage change calculated?

Percentage change is calculated as new value minus old value, divided by the old value, then multiplied by 100.

What is the difference between percentage and percentage points?

Percentage points measure the direct difference between two percentages. Percentage change measures the relative increase or decrease from the original value.

Can percentages be over 100%?

Yes. A percentage over 100% means the value is larger than the original whole. For example, 150% means one and a half times the original.