Key takeaway
To relate two numbers as a percentage, divide one by the other and ×100: A as % of B = (A ÷ B) × 100. The direction matters — 30 as % of 120 = 25%, while 120 as % of 30 = 400%. State which number is the base before calculating.
Scope and assumptions
General arithmetic. 'Percentage of two numbers' here means one as a share of the other, not percent change. This site is informational and not official.
Short answer: To relate two numbers as a percentage, divide one by the other and ×100: A as % of B = (A ÷ B) × 100. The direction matters — 30 as % of 120 = 25%, while 120 as % of 30 = 400%. State which number is the base before calculating. This page handles the two-number comparison view — both directions (A as % of B and B as % of A) — within the same part-over-whole idea as X Is What Percent of Y; for the "A of B" notation see What Percentage Is A of B, and for a ratio stated as a:b see Convert Ratio to Percentage.
Quick navigation
- X is what % of Y → x-is-what-percent-of-y
- % change → percent-change-between-two-numbers
- The formula → percentage-formula
- The calculator → Percentage Calculator
1. Pick a direction
With two numbers A and B, you can ask either:
- A as a % of B → (A ÷ B) × 100
- B as a % of A → (B ÷ A) × 100
They are not the same unless A = B.
2. Worked pairs
| Ask | Formula | Result |
|---|---|---|
| 30 as % of 120 | (30÷120)×100 | 25% |
| 120 as % of 30 | (120÷30)×100 | 400% |
| 45 as % of 60 | (45÷60)×100 | 75% |
| 60 as % of 45 | (60÷45)×100 | 133% |
3. A budget example
A project budget is $120; you have spent $30.
Spent as % of budget = (30 ÷ 120) × 100 = 25%
The remaining $90 is 75% of the budget — the other direction.
4. Watch the base
The number you divide by is the base (the "whole"). Swapping A and B inverts the percentage and can look wildly wrong (25% vs 400%). Always name the base in your answer.
5. Common mistakes
- Wrong direction — (A÷B) vs (B÷A) give different answers; pick deliberately.
- Forgetting ×100 — the division yields a decimal, not a percent.
- Confusing with percent change — this is a share, not a before/after move (see percent-change-between-two-numbers).
- Using unequal units — both numbers must be in the same unit.
6. Both directions matter
With two numbers you can ask either way, and the answers differ. 30 as % of 120 is 25%; 120 as % of 30 is 400%. State the direction every time: "A as a percent of B" uses B as the base. A common reporting error is to give 25% when the reader needed 400%, or vice versa, because the base was assumed instead of stated. Name the base and the ambiguity disappears.
7. Name the base out loud
With two numbers, say the base before you divide: "30 as a percent of 120 — base 120". Then 30 ÷ 120 = 25%. Saying it forces you to choose a direction, and the choice is exactly what most people skip. The same pair can be 25% or 400% depending on which is the base, so the spoken base is not a formality — it is the answer. Make it a habit on every two-number question and the direction errors that produce four-figure percents simply stop happening, because the base was named before the arithmetic began.
8. Two questions, two answers
Two numbers support two different percent questions, and they return two different numbers. "A as a percent of B" and "B as a percent of A" are both valid; they are just not the same answer. Stating which question you mean is not politeness — it is the difference between 25% and 400% on the identical pair. Whenever you present a two-number percent, label the direction, because the reader cannot reconstruct it from the result alone and will guess, usually wrong, about which number was the base.
FAQ
Q: How do I calculate the percentage of two numbers? Divide the first by the second and ×100: (A ÷ B) × 100. Direction decides the answer.
Q: What percent is 30 of 120? (30 ÷ 120) × 100 = 25%.
Q: Can it be over 100%? Yes — if the first number is larger than the base. 120 of 30 = 400%.
Q: Is this the same as percent change? No. This is one number as a share of another; percent change compares an old and new value.
Sources: Khan Academy percentage basics; Maths is Fun — Introduction to Percentages.
Disclaimer: General arithmetic. 'Percentage of two numbers' here means one as a share of the other, not percent change. 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