Example 1
- 15% of 200
30
What is 15% of 200? 30; 170 remains; after an increase 230.
Percentage Calculator
Pick a question and enter two numbers. The calculator finds a percent of a number: 15% of 200 = 30; 20% of 150 = 30. The same fields also answer “what percent”, “of what number”, the value after an increase or decrease, and the original before that change.
Results
Pick a question and enter two numbers. The result appears here.
Old versus new values: percentage change. Invoice tax: VAT calculator.
How the results are calculated
Number200
Percent15%
Part30
The calculator uses the numbers you enter and the question you pick. “p% of n” is (p ÷ 100) × n. 15% of 200 is 0.15 × 200 = 30. “What percent” is part ÷ whole × 100: 30 of 200 is 15%. “Of what number” is part ÷ (p ÷ 100): 30 at 15% is 200.
In Advanced options the second percent is sequential, not applied to the same base. After taking 20% off 100, 80 remains. Then after taking 10% off 80, 72 remains. That is not 30% of 100. Two markups of 20% then 10% on 100 give 132: 100 × 1.20 × 1.10. In “after an increase”, 100 and 20% give a primary result of 120, and two discounts still give 72, not 108. The second percent is used only with p% of n, after an increase, or after a decrease.
Remainder is the number minus the part, which is n × (1 − p ÷ 100). At 200 and 15%, 170 remains. That is the same number as after a decrease. After an increase it is 200 × 1.15 = 230.
Percentage change compares an old value with a new one. Invoice VAT is on a separate page. This page stays with hundredths arithmetic. After an increase the number is n × (1 + p ÷ 100): 200 × 1.15 = 230. After a decrease, 200 × 0.85 = 170. The original before an increase is the result ÷ (1 + p ÷ 100): 230 ÷ 1.15 = 200. Before a decrease, 170 ÷ 0.85 = 200.
Enter 200 and 15. After both numbers the result is 30. The Calculate button does the same. Then “what percent” with 30 and 200: 15%.
Theory, percent, and hundredths arithmetic
Definition
A percent is a hundredth of a whole: p% = p/100 as a decimal. This calculator answers several equivalent questions from that arithmetic. Mode “p% of n”: result = (p/100)×n. “What percent”: p = (part/whole)×100 when whole ≠ 0. “Of what number”: n = part / (p/100) when p ≠ 0. After an increase: n×(1 + p/100); after a decrease: n×(1 − p/100). Before an increase: result/(1 + p/100); before a decrease: result/(1 − p/100), excluding a zero divisor.
The pack(n,p) path computes part = n×p/100, rest = n − part, up = n×(1+p/100), down = n×(1−p/100). An optional second percent (only in of / afterup / afterdown) applies in sequence from the starting number: n×f₁×f₂ with f = 1±p/100 — successive factors on the same starting n.
The primary result depends on the chosen question. Comparing an old value with a new one (percentage change) and invoice VAT live on separate pages.
Historical and conceptual context
Percent comes from Latin per centum (“by the hundred”). Modern % notation and commercial arithmetic (discounts, interest, fees) spread hundredths across Europe from the sixteenth to eighteenth centuries. Mathematically a percent scales a fraction; it is not a separate number enter beyond ℚ/ℝ.
Keep separate: (1) a part of a whole; (2) what percent a part is; (3) recovering the whole from a part and a percent; (4) growth/decay factors 1±p/100; (5) two percents in a row as a product of factors — not the sum of percents off the same base. Percentage points (a difference of two rates) are a different concept.
MathWorld and Wikipedia codify percentage as hundredths; school texts link it to proportion and the rule of three. The related percentage-change calculator compares old and new values in the same hundredths language. Attendance on a separate page is also a percent, but it concerns sessions attended in a fixed schedule, not a discount on a number.
Formal properties
For n, p in ℝ (floating-point in practice): part = np/100. rest = n(1 − p/100). up = n(1 + p/100). down = n(1 − p/100). Inverses: when p ≠ 0, n = part/(p/100); when 1+p/100 ≠ 0, n₀ = up/(1+p/100); when 1−p/100 ≠ 0, n₀ = down/(1−p/100).
Successive discounts: n(1−p₁/100)(1−p₂/100) is generally not n(1 − (p₁+p₂)/100). Example: 100×0.80×0.90 = 72, while 30% off 100 leaves 70. Successive markups: 100×1.20×1.10 = 132.
Modes whatpct / ofwhat / before* ignore the second percent (seqIgnored). Division by a zero whole or percent in the matching modes returns a form error.
Full derivation
Step 1. Pick a question and enter two numbers.
Step 2 (p% of n). 15% of 200: 0.15×200 = 30; remainder 170; after an increase 230. 12.5% of 80: 0.125×80 = 10.
Step 3 (what %). 30 of 200: 30/200×100 = 15%.
Step 4 (of what / before). 30 at 15%: 30/0.15 = 200. 230 after a 15% increase: 230/1.15 = 200. 170 after a 15% decrease: 170/0.85 = 200.
Step 5 (in a row). 100, 20% then 10% as discounts: 100×0.80×0.90 = 72. As markups: 100×1.20×1.10 = 132. In “after an increase”, 100 and 20 give primary 120, while two discounts still yield 72 from starting 100.
Special cases
p = 0 in “p% of n” yields part 0. p = 100 after a decrease yields 0; recovering the original after a 100% decrease has no divisor. p = −100 on an increase blocks recovering the original. Whole 0 in “what %” is an error.
Fractional percents (12.5%) are allowed. Negative n or p are real numbers — the calculator does not force a finance story. Invalid text (for example 15x) shows a message.
The calculator does not compute period compound interest or invoice VAT — those are separate calculators.
Numerical and computational notes
Arithmetic runs in floating-point arithmetic; display uses Intl with en-US (period). The calculator accepts a comma, a period, and typographic minus signs. The second percent applies only when the mode allows it.
Extreme |n| may lose precision, but typical school and retail examples (15% of 200) match paper arithmetic after display rounding.
In teaching, stress the difference between summing percents off one base and multiplying successive factors — the usual mistake behind “20% off, then 10% off.”
The calculator uses only the numbers you enter and the question you pick. In “p% of n” the result is the part; in “what percent” it is p; in “of what” and “before the change” it is the recovered original. Remainder, after-increase, and after-decrease extras follow rest, up, and down from the same (n, p) pair. There is no separate percentage-point model and no tax-rate table on this page.
Related ideas and sources
Related: percentage change, compound percent, VAT, rule of three, attendance (percent present). Related in theory: fraction, proportion, growth factor.
Sources: Wikipedia — Percentage; MathWorld — Percentage; NIST / school arithmetic texts (hundredths); materials on successive discounts (product of factors). Educational tool.
How to use
- Pick a question: a part of a number, what percent, of what number, after an increase or decrease, or the original before that change.
- Enter two numbers. For 15% of 200 enter 200 and 15. For “before the increase” enter 230 and 15.
- Optionally add a second percent with p% of n or after a p% change: successive discounts (100, 20 and 10 → 72) or markups (→ 132). The second percent is used in sequence from the starting number, not from the after-increase result.
- The result updates after both valid numbers are entered. An invalid entry (for example 15x) shows a message. Example 1 is 30, remainder 170, after an increase 230.
- Example 4: 230 after a 15% increase came from 200.
- Example 5: 100 after 20% off, then 10% off, leaves 72.
- Compare an old value with a new one on the percentage-change page.
Percent: a slice of a whole
15% of 200 is 30. 30 of 200 is 15%. 30 at 15% is 200. 200 after a 15% increase is 230. 230 before that increase is 200.
- p% of n
- 0.15 × 200 = 30. Remainder 170 (200 × 0.85 — the same formula as a decrease). After an increase 230.
- what %
- 30 ÷ 200 × 100 = 15. That is not percentage points.
- of what
- 30 ÷ 0.15 = 200. Percent zero has no divisor in this question.
- before the change
- 230 ÷ 1.15 = 200. 170 ÷ 0.85 = 200.
- in a row
- 100 × 0.80 × 0.90 = 72. That is not 30% off the same 100, which would leave 70.
Usage examples
Example 2
- 12.5% of 80
10
What is 12.5% of 80? 10 (one eighth).
Example 3
- 30 of 200 — what percent
15%
What percent of 200 is 30? 15%.
Example 4
- 230 after a 15% increase — original number
200
What was the number before a 15% increase to 230? 200.
Example 5
- 20% off, then 10% off 100 — successive discounts
72
100 × 0.80 × 0.90 = 72. That is not 70, which would be 30% off the same 100. It is also not 108, which would follow if the second discount started from the after-increase result.
Related calculators
Common questions
What is 15% of 200?
30. The calculator uses 0.15 × 200. 170 remains. After a 15% increase the total is 230.
What is 12.5% of 80?
10. 12.5% is one eighth, so 80 ÷ 8 = 10.
What percent of 200 is 30?
15%. In “what percent” mode divide the part by the whole and multiply by 100: 30 ÷ 200 × 100.
30 is 15% of what number?
200. In “of what number” mode divide the part by the percent as a decimal: 30 ÷ 0.15 = 200.
What is left of 100 after 20% off, then 10% off?
72. Use the advanced second percent as a discount: 100 × 0.80 × 0.90. As a markup: 100 × 1.20 × 1.10 = 132. 20% and 10% are not added into 30% of the same base. The chain starts from the starting number: 100 after a 20% increase is 120, and two discounts still give 72, not 108. The second percent is used with p% of n, after an increase, or after a decrease.
Do I enter a % next to 15?
No. The percent field already treats the value as hundredths. 15 means 15%. A leading or trailing percent sign is ignored, so 15% is still 15.
How is this different from percentage change?
Here you compute a slice of one number, the number after an increase or decrease, or the original before that change. Change needs old and new: 5,000 to 5,750 is plus 15% on that page.
Is a negative percent allowed?
Yes. Minus 10% of 200 is −20. 220 remains, because you subtract a negative part.
What is left of 200 after taking 15%?
170. That is the number minus the part: 200 − 30. In “p% of n” the Remainder field shows this difference. In “after a decrease” it is the main result.
What is 200 after a 15% increase?
230. Compute 200 × 1.15. In “p% of n” the After an increase field shows that product. In “after an increase” it is the main result.
Do comma decimals work?
Yes. 12.5 and 12,5 are the same percent. Both give 10 from 80. One thousand is 1000, 1 000, or 1,000. On this English page 1.000 is one; 1,000 is a thousand.
Does the money label change 15% of 200?
No. 30 comes from the numbers. The currency and unit settings in the page header do not affect this result.
230 is the number after a 15% increase. What was the number?
200. Divide 230 by 1.15. In “before the increase” enter 230 and 15.
170 is the number after a 15% decrease. What was the number?
200. Divide 170 by 0.85. In “before the decrease” enter 170 and 15.
What if a field is blank or invalid?
If you click Calculate with a blank field, the calculator asks you to fill both. An invalid number or second percent (for example 15x) shows a message immediately, even if the other field is still empty. Zero in the number field for “p% of n” gives 0.
How do I calculate a percentage of a number?
Multiply the number by the percent and divide by 100: result = n × p / 100. 15% of 200: 200 × 15 / 100 = 30. 20% of 150: 150 × 0.20 = 30. In “What is p% of a number?” enter n and p.
What is 20% of 150?
30. Formula: 150 × 20 / 100. Same mode as 15% of 200 — choose “What is p% of a number?”, enter 150 and 20.
How do I add a percent to a number or take a discount?
After an increase: n × (1 + p/100). After a decrease: n × (1 − p/100). 200 + 15% = 230; 200 − 15% = 170. Pick “after an increase” or “after a decrease”, or read the helper fields in “p% of n”.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100: 30 ÷ 200 × 100 = 15%. Choose “What percent?” and enter 30 and 200.
Why don’t two discounts of 20% and 10% equal 30% off the same base?
Because the second percent acts on the already reduced number. From 100: 100 × 0.80 × 0.90 = 72, not 70. In advanced options enter the second percent as a discount; it starts from the original number, not from an increase result.
Knowledge sources
The formula is the definition of a percent. Below is the vocabulary, not a price list.
Page Updated November 2, 2026.