How to Calculate Percentages: Formulas & Examples
Learn percentage formulas for X% of a number, adding or subtracting percentages, percent change, unknown wholes, and original values with worked examples.
What a Percentage Means
A percentage expresses an amount per 100. The symbol 15% means 15 out of 100, or 0.15 as a decimal. Most percentage mistakes happen because the wrong number is used as the base, so first identify the whole, starting value, or old value named by the problem.
The Percentage Calculator applies the formulas below and updates as soon as both required values are entered.
Percentage Formulas at a Glance
| What you need | Formula | Required condition |
|---|---|---|
| X% of Y | (X ÷ 100) × Y | Finite numbers |
| X is what % of Y? | (X ÷ Y) × 100 | Y cannot be zero |
| Percentage change | ((new − old) ÷ old) × 100 | Old value must be above zero |
| Add P% | starting value × (1 + P ÷ 100) | Finite numbers |
| Subtract P% | starting value × (1 − P ÷ 100) | Finite numbers |
| X is P% of what? | X ÷ (P ÷ 100) | P cannot be zero |
| Original before a P% increase | final value ÷ (1 + P ÷ 100) | P must be zero or greater |
| Original before a P% decrease | final value ÷ (1 − P ÷ 100) | 0 ≤ P < 100 |
Find a Percentage of a Number
Convert the percentage to a decimal, then multiply it by the number. For 15% of 200:
This is useful for finding a tip, tax amount, commission, or one part of a larger value. Keep the unit of the whole: 15% of $200 is $30, while 15% of 200 kg is 30 kg.
Find What Percent One Number Is of Another
Divide the part by the whole and multiply by 100. If 30 questions out of 200 belong to one category:
The whole cannot be zero because division by zero is undefined. Also make sure the part and whole use the same unit before comparing them.
Add or Subtract a Percentage
Add a percentage
To add 20% to 100, multiply by 1.20. The 1 keeps the original value and 0.20 adds the increase.
Subtract a percentage
To subtract 20% from 100, multiply by 0.80. The remaining share is 100% − 20% = 80%.
Equal increases and decreases do not cancel because the second operation uses a different base. Adding 20% to 100 gives 120, and subtracting 20% of 120 gives 96. To recover the original, use a reverse formula instead.
Calculate Percentage Change
Percentage change compares the difference with the old value. A positive answer is an increase; a negative answer is a decrease. If a value rises from 80,000 to 96,000:
Standard percentage change is undefined when the old value is zero, because the formula would divide by zero. In that case, report the absolute change or explain the new value without assigning a standard percentage increase.
Reverse a Percentage
Find the unknown whole
If 60 is 30% of an unknown number, divide 60 by 0.30:
Find the original before an increase
A final value of 120 after a 20% increase represents 120% of the original. Divide by 1.20:
Find the original before a decrease
A final value of 80 after a 20% decrease represents 80% of the original. Divide by 0.80:
A 100% decrease cannot be reversed to one unique value: every starting value would end at zero. Reverse-decrease mode therefore accepts rates from zero up to, but not including, 100%.
Percentage Points vs. Percentage Change
If a rate moves from 20% to 30%, it rises by 10 percentage points. Relative to the original 20%, however, the percentage increase is 50%: (30 − 20) ÷ 20 × 100. Use “percentage points” for the direct difference between two percentages and “percentage change” for the relative movement.
Precision, Rounding, and Common Mistakes
- Keep full precision during the calculation and round only the final answer. The calculator displays ordinary answers with up to four decimal places and preserves very small nonzero answers with additional precision or scientific notation.
- Confirm the base: old value for percentage change, whole for a part-to-whole comparison, and final value for a reverse calculation.
- Do not reverse an increase by subtracting the same percentage. Divide by the growth multiplier instead.
- Compare like units. Convert measurements or currencies before calculating a percentage relationship.
Use the Matching Calculator Mode
Use the Percentage Calculator for the eight operations covered here. For shopping offers with stacked discounts and tax, use the Discount Calculator so each discount is applied to the correct remaining price.
Related Calculators
FAQs
How do I calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. For example, 15% of 200 is 0.15 × 200 = 30.
How do I add or subtract a percentage?
To add P%, multiply the starting value by 1 + P/100. To subtract P%, multiply by 1 - P/100.
How do I reverse a percentage increase or decrease?
Divide the final value by 1 + P/100 to reverse an increase, or by 1 - P/100 to reverse a decrease below 100%.
Why do equal percentage increases and decreases not cancel?
The second percentage uses the changed value as its base. Adding 20% to 100 gives 120, then subtracting 20% of 120 gives 96, not 100.
Can I recover a value before a 100% decrease?
No. Every starting value becomes zero after a 100% decrease, so a final value of zero does not reveal one unique original value.
What is the percentage change from zero?
Standard percentage change divides by the old value, so it is undefined when the old value is zero. Report the absolute change or use another comparison instead.