How do I calculate X% of a number?

Multiply the number by the percent written as a decimal. Example: 15% of 200 = 200 x 0.15 = 30.

How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100. Example: 25 is what percent of 200? 25 / 200 x 100 = 12.5%.

How do I work backwards from a percentage?

If you know the part and the percent, divide the part by the percent as a decimal. Example: 45 is 15% of what? 45 / 0.15 = 300.

What is the formula for percentage change?

Percentage change = ((new value - old value) / old value) x 100. Positive results mean an increase, and negative results mean a decrease.

What is percent error?

Percent error compares a measured value with an expected value using |measured - expected| / |expected| x 100. Example: 9.8 measured versus 10 expected equals 2% error.

How do stacked discounts work?

Stacked discounts are applied one after another, not added together. A 20% discount followed by 10% off is an effective 28% discount because the second discount applies to the reduced price.

Percentage Calculator

Calculate percentages fast: find X% of Y, what percent X is of Y, reverse percentages, percentage change, percentage difference, percent increase or decrease, and stacked discounts.

Quick examples

Load a common calculation, then edit the numbers to match your situation.

What is X% of Y?

Use this for tips, discounts, tax, commissions, and simple markups.

Percent Of

Result

—

Enter both values, then select Calculate.

X is what % of Y?

Useful for test scores, budget share, conversion rates, and win rates.

Part Whole

Result

—

Enter both values, then select Calculate.

X is P% of what?

Work backwards from commissions, discounts, taxes, and split amounts.

Part Percent

Result

—

Enter the part and percent, then select Calculate.

Percentage change

Compare a new value against a starting value to measure increase or decrease.

From To

Result

—

Enter both values, then select Calculate.

Percentage difference

Compare two values without treating either one as the starting point.

Value 1 Value 2

Result

—

Enter both values, then select Calculate.

Percent error

Compare a measured result against an expected value for labs, forecasts, and quality checks.

Measured value Expected value

Result

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Enter both values, then select Calculate.

Increase or decrease a value by a percent

Great for markups, markdowns, raises, inflation checks, and quick scenario planning.

Starting value Percent Action

Result

—

Enter a value and percent, then select Calculate.

Percent off with extra discounts

See the final sale price when a base discount is followed by one or two extra coupons.

Original price Discount 1 (%) Discount 2 (%)

Discount 3 (%) optional

Final price

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Enter the original price and at least one discount, then select Calculate.

Percentage formulas at a glance

Percent of a value

result = (percent ÷ 100) × value

Example: 20% of 45 = 0.20 × 45 = 9.

What percent?

percent = (part ÷ whole) × 100

Example: 42 out of 50 = 84%.

Reverse percentage

whole = part ÷ (percent ÷ 100)

Example: 45 is 15% of 300.

Percentage change

((new − old) ÷ |old|) × 100

Example: 80 to 100 = 25% increase.

Percentage difference

|a − b| ÷ ((|a| + |b|) ÷ 2) × 100

Example: 48 and 60 differ by 22.22%.

Percent error

|measured − expected| ÷ |expected| × 100

Example: 9.8 versus 10 gives a 2% error.

Increase or decrease by percent

new value = value × (1 ± percent ÷ 100)

Example: 120 increased by 15% = 138.

Stacked discounts

sale price = original × (1 − d1) × (1 − d2) × ...

Example: 20% off then 10% off = 28% off overall, not 30%.

When to use each percentage workflow

What is X% of Y? for tips, discounts, sales tax, commission, and simple markups.
X is what % of Y? for exam scores, savings rates, ad conversion rates, and completion percentages.
X is P% of what? when you know the partial amount and need the original total.
Percentage change when one number clearly comes before the other, like revenue last month versus this month.
Percentage difference when you are comparing two values as peers, such as lab measurements or supplier quotes.
Percent error when one number is the expected target and the other is the observed result.
Increase or decrease by percent when you want the new value after a raise, markdown, fee, or inflation change.
Percent off with extra discounts when a coupon stacks on top of a sale price.

Percentage change vs percentage difference

These two formulas are often confused. Percentage change uses the starting value as the baseline, which makes it ideal for growth and decline over time. Percentage difference uses the average of the two values as the baseline, which makes it better for side-by-side comparisons where neither value should be treated as the original.

Why stacked discounts are not additive

If a store offers 20% off and then an extra 10% coupon, the second discount applies to the already reduced price. That means a 20% discount followed by 10% off produces an effective 28% discount, not 30%. This tool shows each step so you can explain the math to customers, teammates, or students.

Common percentage examples

Scenario	Calculation	Answer
Restaurant tip	20% of 45	9
Test score	42 is what % of 50	84%
Sale price planning	45 is 15% of what	300
Traffic growth	80 to 100	25% increase
Supplier quote comparison	48 vs 60	22.22% difference
Lab measurement	9.8 measured vs 10 expected	2% error
Markup planning	Increase 120 by 15%	138
Coupon stacking	120 with 20% off, then 10% off	86.4

Tips for calculating percentages accurately

Use percentage change only when one number is the original value and the other is the new value.
If you want the original total from a percent amount, use the reverse percentage mode instead of percentage change.
When combining discounts, apply them one at a time instead of adding the percentages together.
Round for display, but keep more decimal places when you need precise budgeting, analytics, or lab comparisons.
For percent error, the expected value is the baseline. If the expected value is 0, use an absolute error instead of a percent.
Negative values can produce surprising percentage changes because the baseline matters. Double-check the business meaning before using them in reports.