Key takeaway
To calculate a percentage, use (part ÷ whole) × 100 for a part of a total, (percent ÷ 100) × number for a percent of a number, and ((new − old) ÷ old) × 100 for percent change. The single biggest error is dividing by the wrong base — always confirm which number is the 'whole'.
Scope and assumptions
These are general arithmetic methods; specific grading, tax, or financial rules may use different bases. Confirm the exact scheme in your context. This site is informational and not official.
Short answer: Use (part ÷ whole) × 100 for "what percent is X of Y", (percent ÷ 100) × number for "what is P% of N", and ((new − old) ÷ old) × 100 for change. Pick the formula by the question, then keep the base straight. This page is the step-by-step how-to; for the formula reference and derivations (why % means ÷100) see Percentage Formula.
Quick navigation
- The formula → percentage-formula
- What a % is → what-is-a-percentage
- % of a number → percentage-of-a-number
- The calculator → Percentage Calculator
1. The three situations
Most "calculate percentage" questions fall into one of three shapes:
| Situation | Formula | Example |
|---|---|---|
| Part of a whole | (part ÷ whole) × 100 | 20 of 50 = 40% |
| Percent of a number | (percent ÷ 100) × number | 20% of 50 = 10 |
| Percent change | ((new − old) ÷ old) × 100 | 50 → 60 = +20% |
The rest of this guide shows each one with a worked example and the trap that breaks it.
2. Part of a whole
You scored 20 out of 50. The "whole" is 50, the "part" is 20.
% = (20 ÷ 50) × 100 = 40%
The whole is always the denominator — points possible, total items, the full amount. If you flip them (50 ÷ 20) you get 250%, which is not the percentage you meant.
3. Percent of a number
What is 20% of 50? Turn 20% into 0.20, then multiply:
0.20 × 50 = 10
So 20% of 50 is 10. This is the form used for "how much is the tip / the discount / the tax". Note it is different from "20 out of 50" — that one is 40%, not 10.
4. Percent change
A price moves from $50 to $60. Old = 50, new = 60.
((60 − 50) ÷ 50) × 100 = 20% — a 20% increase.
If it fell $60 → $50, the same formula gives −16.7% (a decrease). The base is the old value, never the new one — using 50 (the new value) as the base would wrongly give −20%.
5. Worked examples
| You have | Ask | Formula | Result |
|---|---|---|---|
| 18 / 20 | % | (18÷20)×100 | 90% |
| 15% of 200 | value | 0.15×200 | 30 |
| 80 → 100 | change | ((100−80)÷80)×100 | +25% |
| 100 → 80 | change | ((80−100)÷100)×100 | −20% |
6. Common mistakes
- Wrong base — dividing by the part instead of the whole gives a number >100% that isn't the percentage you meant.
- Forgetting ÷100 — 20 × 50 = 1000, not 20% of 50; you must convert the % to 0.20 first.
- Using the new value as base in change — change is always relative to the old number.
- Mixing up the two percent questions — "20% of 50" (answer 10) is not "20 of 50" (answer 40%).
- Rounding before the final step — round only the displayed percentage, not the intermediate division.
7. A 30-second formula picker
Not sure which formula fits? Match the question to the row:
| Your question | Formula |
|---|---|
| What share is this? | (part ÷ whole) × 100 |
| How much is P% of N? | (P ÷ 100) × N |
| How much did it change? | ((new − old) ÷ old) × 100 |
| What was the original? | final ÷ (1 − r) |
Keep the base straight and every percentage question resolves to one of these four. Practice by naming the base out loud before you calculate — most errors start with the wrong one.
FAQ
Q: What is the basic percentage formula? (part ÷ whole) × 100 — use this when you have a part of a total.
Q: How do I find a percent of a number? Convert the percent to a decimal (÷100) and multiply: 20% of 50 = 0.20 × 50 = 10.
Q: Why is my percent change negative? Because the value dropped. A fall from 100 to 80 is ((80−100)÷100)×100 = −20%.
Q: What base do I divide by? The whole, or the old value for change — never the part and never the new value.
Q: Is a percentage the same as a fraction? A percentage is a fraction out of 100 (40% = 40/100 = 0.40); different notations for the same idea.
Sources: Khan Academy percentage basics; Maths is Fun — Introduction to Percentages.
Disclaimer: These are general arithmetic methods; specific grading, tax, or financial rules may use different bases. Confirm the exact scheme in your context. This site is informational and not official.
Sources and references
- Khan Academy percentage basicshttps://www.khanacademy.org/math/pre-algebra/x31947de81e3f6453:percentages
- Maths is Fun — Introduction to Percentageshttps://www.mathsisfun.com/percentage.html