Rule of Three Calculator

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rule of three for percentage

Rule of Three for Percentages

Every percentage question is a proportion with one quantity fixed at 100. To find how much X% of a total Y is, set A=100, B=Y, C=X and solve X = B×C/A; to find what percentage a part represents of the total, swap B and C in the setup.

Two directions of the same proportion

In the most common direction, "how much is X% of Y", the proportion reads 100 is to Y as X is to the result: to find 20% of 80, A=100, B=80, C=20, and X=(80×20)/100=16. In the opposite direction, "what percentage does A represent of B", the role of 100 moves: to find what percentage $45 represents of $300, use A=300, B=100, C=45, giving X=(100×45)/300=15, that is, 15%. The same direct rule of three serves both questions, only which quantity fills which position changes.
Commission and discount calculations follow the same direct logic. A 7.5% commission on a $1,240 sale is A=100, B=1240, C=7.5, giving X=(1240×7.5)/100=93, or $93. Because it is a direct proportion (the larger the sale, the larger the commission in dollars), the result grows and shrinks at the same rate as the sale value: doubling the sale to $2,480 doubles the commission to $186, keeping the same 7.5% rate.
The percentage rule of three calculates a fixed fraction of one value, not compound growth across several periods: for interest or adjustments that accumulate over more than one step, each round's percentage applies to a different total, and this simple proportion alone does not capture that. For a single percentage applied to a single total, though, the direct rule of three described here gives the exact result, with no approximation.

Examples

How much is 20% of 80

Input: A=100, B=80, C=20
Expected output: X = 16

100 is to 80 as 20 is to X; 80×20÷100=16, so 20% of 80 is 16.

What percentage is $45 of $300

Input: A=300, B=100, C=45
Expected output: X = 15

Here 100 sits in position B, not A; 100×45÷300=15, so $45 is 15% of $300.

A 7.5% commission on a $1,240 sale

Input: A=100, B=1240, C=7.5
Expected output: X = 93

1240×7.5÷100=93; doubling the sale to $2,480 doubles the commission to $186, keeping the same 7.5% rate.

Full tool FAQ

What is a direct rule of three?

In a direct proportion, two quantities grow or shrink together: doubling one doubles the other. You set up A/B = C/X and isolate the unknown with X = B × C / A. For example, if 3 workers produce 6 items per day, 5 workers produce X = 6 × 5 / 3 = 10 items, because more labor yields more output in the same proportion.

What is an inverse rule of three?

How do I tell direct from inverse?

What is a compound rule of three?

Can I use decimal values?

What happens if I divide by zero?

How do I use it for unit conversion?

Does the tool round the result?

Frequently asked questions

How do I know which position gets the value 100?

If the question is "how much is X% of Y", 100 goes in A and Y goes in B. If the question is "what percentage does a part represent of a total", 100 goes in B and the total goes in A; swapping those positions gives a wrong result.

Does this rule of three work for compound interest?

Not directly. It calculates a fixed fraction of a single total (a simple direct proportion); compound interest applies the percentage repeatedly to a balance that changes every period, which requires exponentiation, not just this proportion.

Does the result change if I use a comma or a period to separate decimals in the percentage?

No, as long as the numeric value is the same: 7.5% and 7,5% represent the same fraction of 0.075. What matters for the result is the number, not the decimal separator used to type it.

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rule of three for percentage

Rule of Three for Percentages

Two directions of the same proportion

In the most common direction, "how much is X% of Y", the proportion reads 100 is to Y as X is to the result: to find 20% of 80, A=100, B=80, C=20, and X=(80×20)/100=16. In the opposite direction, "what percentage does A represent of B", the role of 100 moves: to find what percentage $45 represents of $300, use A=300, B=100, C=45, giving X=(100×45)/300=15, that is, 15%. The same direct rule of three serves both questions, only which quantity fills which position changes.

Commission and discount calculations follow the same direct logic. A 7.5% commission on a $1,240 sale is A=100, B=1240, C=7.5, giving X=(1240×7.5)/100=93, or $93. Because it is a direct proportion (the larger the sale, the larger the commission in dollars), the result grows and shrinks at the same rate as the sale value: doubling the sale to $2,480 doubles the commission to $186, keeping the same 7.5% rate.

The percentage rule of three calculates a fixed fraction of one value, not compound growth across several periods: for interest or adjustments that accumulate over more than one step, each round's percentage applies to a different total, and this simple proportion alone does not capture that. For a single percentage applied to a single total, though, the direct rule of three described here gives the exact result, with no approximation.

Examples

How much is 20% of 80

Input: A=100, B=80, C=20
Expected output: X = 16

100 is to 80 as 20 is to X; 80×20÷100=16, so 20% of 80 is 16.

What percentage is $45 of $300

Input: A=300, B=100, C=45
Expected output: X = 15

Here 100 sits in position B, not A; 100×45÷300=15, so $45 is 15% of $300.

A 7.5% commission on a $1,240 sale

Input: A=100, B=1240, C=7.5
Expected output: X = 93

1240×7.5÷100=93; doubling the sale to $2,480 doubles the commission to $186, keeping the same 7.5% rate.

Full tool FAQ

What is a direct rule of three?

What is an inverse rule of three?

How do I tell direct from inverse?

What is a compound rule of three?

Can I use decimal values?

What happens if I divide by zero?

How do I use it for unit conversion?

Does the tool round the result?

Frequently asked questions

How do I know which position gets the value 100?

Does this rule of three work for compound interest?

Does the result change if I use a comma or a period to separate decimals in the percentage?

No, as long as the numeric value is the same: 7.5% and 7,5% represent the same fraction of 0.075. What matters for the result is the number, not the decimal separator used to type it.