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 the simple rule of three?

It is the method for finding a fourth value when two quantities are proportional and you know three numbers. You set up a table with two rows (two situations) and two columns (the quantities), leave one value as the unknown x and solve. If 4 kg cost $20, how much do 7 kg cost? The price per kilo is 20 ÷ 4 = 5, so 7 kg cost 7 × 5 = $35.

What is a direct rule of three? Give an example.

What is an inverse rule of three? Give an example.

How do I know whether the rule of three is direct or inverse?

What is the compound rule of three?

How do I solve the compound rule of three step by step?

How do I check the result with the cross product?

Can I use the rule of three to calculate a percentage?

How do I use the rule of three for map scale, exchange rates and recipes?

Can I type decimals, commas and dots? Is the math exact?

When does the rule of three not work, and what happens with division by zero?

Can any value be the unknown? Can I name the quantities?

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 the simple rule of three?

What is a direct rule of three? Give an example.

What is an inverse rule of three? Give an example.

How do I know whether the rule of three is direct or inverse?

What is the compound rule of three?

How do I solve the compound rule of three step by step?

How do I check the result with the cross product?

Can I use the rule of three to calculate a percentage?

How do I use the rule of three for map scale, exchange rates and recipes?

Can I type decimals, commas and dots? Is the math exact?

When does the rule of three not work, and what happens with division by zero?

Can any value be the unknown? Can I name the quantities?

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.