How to Calculate Percentages

What is the percentage formula?

The percentage formula is part = (percent ÷ 100) × whole. A percent is a ratio expressed per hundred: the word comes from the Latin per centum, and 35% means 35 out of every 100. Converting a percent to a decimal means dividing by 100, which is the same as moving the decimal point two places left, so 35% is 0.35 and 7.5% is 0.075.

Most everyday questions are one of three rearrangements of that single equation. You know the percent and the whole and want the part, you know the part and the whole and want the percent, or you know two values and want the change between them. The percent calculator solves all three: fill in any two of the boxes and it returns the third.

How do you find X percent of a number?

Convert the percent to a decimal and multiply it by the number. For 20% of 80, 20 ÷ 100 = 0.20, and 0.20 × 80 = 16.

A mental shortcut helps for round percents. 10% of any number is that number with the decimal point moved one place left, so 10% of 80 is 8. Double it for 20% (16), halve it for 5% (4), and add the two for 15% (12). The same trick gives a quick tip estimate: 10% of a $46 bill is $4.60, so 20% is $9.20.

Percents also run in both directions: X% of Y always equals Y% of X. 8% of 50 looks awkward, but 50% of 8 is obviously 4, and the two are the same.

How do you calculate what percent one number is of another?

Divide the part by the whole, then multiply by 100. If you answered 15 questions correctly out of 60, 15 ÷ 60 = 0.25, and 0.25 × 100 = 25%.

The order matters. The whole, the number after "of," always goes on the bottom. 60 is 400% of 15, not 25%. When the part is larger than the whole the answer is over 100%, which is normal: a town that grew to 12,000 people from 8,000 is at 150% of its old size.

To work backward from a percent to the whole, divide the part by the decimal. If $30 is 25% of a budget, the full budget is 30 ÷ 0.25 = $120.

What is the percentage increase formula?

Percentage change = (new value − old value) ÷ old value × 100. A positive result is an increase and a negative result is a decrease. The percentage increase calculator shows the change, the absolute difference and the multiplier together.

Worked example: a monthly bill rises from $80 to $100. The difference is $20, and 20 ÷ 80 = 0.25, a 25% increase. The new bill is 125% of the old one, a multiplier of 1.25.

Now reverse it. If the bill falls from $100 back to $80, the change is −20 ÷ 100 = −20%. The same $20 is a smaller share of the larger starting value, which is why a 25% rise and a 20% fall cancel out. Always divide by the value you started from.

How do you calculate percent off a price?

Multiply the original price by (100 − discount) ÷ 100. For 20% off, keep 80% of the price: $60 × 0.80 = $48. The amount you save is the price times the discount, $60 × 0.20 = $12. The percent off calculator returns both numbers at once.

To take 20% off in your head, find 10% (move the decimal one place), double it, and subtract. For a $49.99 item, 10% is about $5, so 20% is about $10 and the sale price is $39.99.

The table shows a $60 item at common discounts, as our percent off calculator computes them.

Do stacked discounts add up?

No. A second discount applies to the already reduced price, so 20% off plus an extra 10% off is a 28% total discount, not 30%. On an $80 item, 20% off gives $64, and 10% off $64 removes another $6.40, for a final price of $57.60. In multipliers, 0.80 × 0.90 = 0.72, so you pay 72% of the original.

The order of two percentage discounts does not change the result, because multiplication is commutative. A fixed-dollar coupon is different: $15 off a $120 item is a 12.5% discount, and taking it before or after a percentage discount does change the total. The discount calculator handles both percent and fixed-amount discounts and shows the equivalent percent off.

What is the difference between percent and percentage points?

A percentage point is the plain arithmetic difference between two percentages, while percent change measures that difference relative to the starting percentage. If a savings rate goes from 4% to 5%, it rose by 1 percentage point, and it also rose by 25%, because 1 ÷ 4 = 0.25.

Both statements are true, but they sound very different, so news reports and financial documents should say which one they mean. Interest rates, unemployment rates, tax rates and poll numbers are usually compared in percentage points. When a rate is small, a modest point change can be a large percent change: a loan rate moving from 2% to 3% is only 1 point but a 50% increase in the rate. For more on how rates are quoted, see APR vs APY.

What mistakes should you avoid with percentages?

Most percentage errors come from dividing by the wrong number or adding percentages that apply to different bases.

• Dividing by the new value instead of the old one when computing percent change.
• Adding successive percentage changes. A 10% gain followed by a 10% loss leaves you at 99% of the start, because 1.10 × 0.90 = 0.99.
• Reversing a discount by adding the same percent back. A $48 sale price is 80% of the original, so the original is 48 ÷ 0.80 = $60, not 48 × 1.20 = $57.60.
• Confusing markup with margin. A 50% markup on cost is a 33.3% margin on price; see profit margin vs markup.
• Mixing up percentage points and percent when comparing rates.