Percentage formulas, with examples
What is X% of Y?
To calculate X% of Y, multiply Y by X and divide by 100.
result = rate × base ÷ 100
Example: An 18% tip on a $64 bill: 18% of 64 = 11.52.
X is what percent of Y?
To find what percent X is of Y, divide X by Y and multiply by 100.
result = part ÷ whole × 100
Example: 38 correct answers out of 50 on a test: 38 as a percentage of 50 = 76%.
Percentage increase from X to Y
To calculate a percentage increase, subtract the initial value from the final value, divide by the initial value and multiply by 100.
result = (final − initial) ÷ initial × 100
Example: Rent that went up from $1,450 to $1,595: Percentage increase from 1,450 to 1,595 = 10%.
Percentage decrease from X to Y
To calculate a percentage decrease, subtract the final value from the initial value, divide by the initial value and multiply by 100.
result = (initial − final) ÷ initial × 100
Example: An investment that fell from $2,500 to $2,100: Percentage decrease from 2,500 to 2,100 = 16%.
Add X% to Y
To add X% to a number, multiply it by (1 + X ÷ 100).
result = base × (1 + rate ÷ 100)
Example: A $1,400 rent with a 5% raise: 1,400 plus 5% = 1,470.
Subtract X% from Y
To subtract X% from a number, multiply it by (1 − X ÷ 100).
result = base × (1 − rate ÷ 100)
Example: An $80 jacket with 25% off: 80 minus 25% = 60.
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Worked examples
| Question | Calculation | Working | Result |
|---|---|---|---|
| How much is an 18% tip on $64? | What is X% of Y? | 18 × 64 ÷ 100 | 11.52 |
| I got 38 out of 50. What is my grade? | X is what percent of Y? | 38 ÷ 50 × 100 | 76% |
| Rent went up from 1,450 to 1,595. By how much? | Percentage increase from X to Y | (1,595 − 1,450) ÷ 1,450 × 100 | 10% |
| Was $80, now $60. What percent off? | Percentage decrease from X to Y | (80 − 60) ÷ 80 × 100 | 25% |
| 1,400 rent going up 5% | Add X% to Y | 1,400 × 1.05 | 1,470 |
| 80 dollars with 25% off | Subtract X% from Y | 80 × 0.75 | 60 |
| I invested 2,000 and now I have 2,600 | Percentage increase from X to Y | (2,600 − 2,000) ÷ 2,000 × 100 | 30% |
| What is 15% of 80? | What is X% of Y? | 15 × 80 ÷ 100 | 12 |
Common percentage mistakes
Going up 10% and then down 10% does not bring you back
100 + 10% = 110, but 110 − 10% = 99. The second 10% is taken from a bigger number, so you end 1% below where you started.
Undoing a discount is not adding the same percent back
If a price after 20% off is $80, the original was $80 ÷ 0.8 = $100, not $80 + 20% = $96.
Percentage change is always measured against the starting value
From 50 to 75 is a 50% increase, but from 75 back to 50 is a 33.33% decrease. Same gap, different base.
Percent and percentage points are different things
An interest rate that moves from 4% to 5% rose by 1 percentage point, which is a 25% increase in the rate itself.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 80 is 80 × 15 ÷ 100 = 12.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 38 out of 50 is 38 ÷ 50 × 100 = 76%.
How do I calculate a percentage increase or decrease?
Take the difference between the two values, divide it by the starting value and multiply by 100. From 80 to 100 is a 25% increase; from 80 to 60 is a 25% decrease.
How do I add or subtract a percentage from a number?
To add X%, multiply by (1 + X ÷ 100); to subtract X%, multiply by (1 − X ÷ 100). So $80 with 25% off is 80 × 0.75 = $60.
Can I just type my question instead of filling in a form?
Yes. Smart mode understands everyday questions such as “how much is an 18% tip on $64?” or “rent went up from 1,450 to 1,595” and picks the right calculation. If it is unsure, it asks you to confirm.
Is my question sent to a server?
The calculation never needs one: smart mode runs a 1.2 MB open-source model (percent-nlu) inside your browser and works offline once loaded. To improve the model, the question and the model’s answer are saved anonymously (no account, no IP address) unless you turn it off under the question field.
What can smart mode not do yet?
It handles the six calculations on this page, with up to four numbers. Chained calculations (“20% off and then 10% tax”), fractions and ranges are not supported yet; use the classic calculators for those steps.
Why is a 10% rise followed by a 10% drop not zero?
Because the drop is taken from the higher value. 100 becomes 110, and 10% of 110 is 11, so you end at 99.
Who made this and how it works
The icupu Percentage Calculator is built by Emanoel S. Vieira. Smart mode runs percent-nlu, an open-source model with 1.16M parameters (1.2 MB) that reads your question, picks one of the six calculations and assigns each number its role. It answers in about 1 to 5 ms on your device; the arithmetic itself is plain code, so it is always exact.
On 118 hand-checked English questions it never saw in training, it got the calculation and every number right 95.7% of the time, and 100% of the answers it gave without asking for confirmation were correct. Read the methodology and limitations.
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