How to use the percentage calculator
Start with the question menu. The box labels change to match what you pick, so you always know which number goes where. Type percentages as plain numbers: 20 means 20%, and 12.5 means 12.5%.
The precision menu only changes how many decimal places you see. The math runs at full precision underneath, so switching from 2 places to 6 won't change the answer, just how much of it shows.
- Choose the percentage question that matches your wording.
- Enter the two numbers the labels ask for.
- Pick how many decimal places to show.
- Press Calculate percentage.
- Read the answer, then check the formula, the base used and the reverse check.
Pick the question that matches your wording
Most percent mistakes come from dividing by the wrong number. The fix is to start from the sentence you're trying to answer. Each question type below uses a different base, the number that counts as 100%.
| Question | You know | You get | Base (100%) |
|---|---|---|---|
| What is P% of X? | X and P | The part | X |
| X is what percent of Y? | Part X and whole Y | The percent | Y |
| X is P% of what number? | Part X and P | The whole | The answer |
| Increase or decrease X by P% | X and P | The new value | X |
| Percentage change from X to Y | Old X and new Y | Percent up or down | X, the starting value |
| Percentage difference between X and Y | Two values | Gap as a percent | Average of X and Y |
| Original before a P% increase or decrease | Final value and P | The original | The original |
| Percentage-point change | Two percentages | Points and basis points | None |
What percent of one number is another?
Divide the part by the whole and multiply by 100. If 30 of 150 people picked an option, that's 30 / 150 x 100 = 20%. If you scored 45 out of 60, you got 75%.
Order matters. 30 is 20% of 150, but 150 is 500% of 30. The whole is whatever the sentence says you're comparing against, which isn't always the bigger number or the newer one.
Percent = part / whole x 100Part = whole x percent / 100Whole = part / (percent / 100)
Percent change calculator: increase or decrease
Percent change measures a move from an old value to a new one, so you always divide by the old value. A rise from 80 to 100 is a 25% increase, because the change of 20 is divided by 80. Going back down from 100 to 80 is a 20% decrease, because now the same 20 is divided by 100.
That's also why equal ups and downs don't cancel. Add 20% to 100 and you get 120. Take 20% off 120 and you get 96, not 100. The calculator's change mode shows the raw difference, the percent and the direction, and it won't divide by a starting value of zero.
Percent change = (new value - old value) / |old value| x 100
Adding or taking off a percentage
To add a percentage, multiply by 1 plus the rate. To take one off, multiply by 1 minus the rate. Increasing 150 by 20% is 150 x 1.20 = 180. Decreasing 150 by 20% is 150 x 0.80 = 120. One multiplication does the whole job.
Going backwards is where people slip. If a price is 120 after a 20% markup, the original was 120 / 1.20 = 100. Taking 20% off 120 gives 96, which is wrong because the markup was 20% of 100, not 20% of 120. Use the reverse modes for this, and they'll divide by the right multiplier.
After an increase = start x (1 + P / 100)After a decrease = start x (1 - P / 100)Original before an increase = final / (1 + P / 100)Original before a decrease = final / (1 - P / 100)
Percent change, percentage difference and percentage points
These three get mixed up all the time. Percent change has a direction and divides by the starting value. Percentage difference has no direction: it divides the gap by the average of the two numbers, so 80 and 100 are 22.2222% apart whichever you list first.
Percentage points are for when both numbers are already percentages. A rate that moves from 4% to 5% went up 1 percentage point, or 100 basis points. Measured against the 4% it started at, that's a 25% relative increase. The points mode shows both so you can say which one you mean.
Percentage difference = |X - Y| / ((|X| + |Y|) / 2) x 100Percentage-point change = new percent - old percent; basis points = points x 100
How to average percentages
Don't add percentages and divide by how many there are unless every percent comes from the same size group. If you scored 80% on a 50-point quiz and 90% on a 150-point exam, the simple average is 85%. But you earned 40 + 135 = 175 of 200 points, which is 87.5%.
To get the true average, turn each percent back into its part with "What is P% of X?", add the parts, add the wholes, and then use "X is what percent of Y?" on the totals. This calculator doesn't have a separate averaging mode, so those two modes are the way to do it here.
Weighted average percent = (sum of parts) / (sum of wholes) x 100
Worked percentage examples
Every row uses small numbers so you can check it in your head. Notice how 150, 20 and 30 answer three different questions depending on what's unknown.
| Question | Setup | Answer |
|---|---|---|
| What is 20% of 150? | 150 x 0.20 | 30 |
| 30 is what percent of 150? | 30 / 150 x 100 | 20% |
| 30 is 20% of what? | 30 / 0.20 | 150 |
| Increase 150 by 20% | 150 x 1.20 | 180 |
| Decrease 150 by 20% | 150 x 0.80 | 120 |
| Percent change from 80 to 100 | 20 / 80 x 100 | 25% increase |
| Percentage difference, 80 and 100 | 20 / 90 x 100 | 22.2222% |
| 120 after a 20% increase | 120 / 1.20 | 100 originally |
| 80 after a 20% decrease | 80 / 0.80 | 100 originally |
| 4% rises to 5% | 5 - 4 | 1 percentage point |
Sources
These references back up the percent change method, percent notation and the difference between percent and percentage points.