Rule of Three Calculator

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inverse rule of three

Inverse Rule of Three

In an inverse proportion, the product of the two quantities stays constant: A × B = C × X, so X = A × B / C. It models situations where increasing one quantity makes the other decrease at the same rate, such as speed and time for a fixed distance.

How the inverse proportion works

For a fixed distance, the higher the speed, the lower the time spent, and the product speed × time always equals that distance. Driving at 80 km/h for 3 h covers 240 km (80×3); keeping that same distance but at 100 km/h, the time drops to X=(80×3)/100=2.4 h, that is, 2 h 24 min, because speed rose 25% and time fell by the matching inverse ratio.
The same logic applies to flow rate: a tank that 3 taps fill in 10 hours has a constant product of 30 (taps × hours). With 5 taps running at once, the time drops to X=30/5=6 hours: raising the number of taps by 67% (from 3 to 5) does not cut the time in half, it shrinks by the exact ratio 5/3, from 10 h to 6 h.
Inverse proportion assumes each extra unit contributes identically to the others, with no coordination overhead: 5 painters finish a job in 12 days, and the product painters × days sits at 60; with only 3 painters, the deadline stretches to X=60/3=20 days. That prediction only holds exactly when the work is perfectly divisible among people; tasks with sequential steps, where one can only start after the previous finishes, do not follow the same proportion no matter how many people are added.

Examples

Speed × time (fixed distance)

Input: A=80, B=3, C=100
Expected output: X = 2.4

At 80 km/h for 3 h the trip covers 240 km; over the same distance at 100 km/h, the time drops to 2.4 h (2 h 24 min).

Taps filling a tank

Input: A=3, B=10, C=5
Expected output: X = 6

3 taps take 10 h; 5 taps keep the product at 30 and finish in 6 h, not by coincidence: 30÷5=6.

Painters finishing a job

Input: A=5, B=12, C=3
Expected output: X = 20

Dropping from 5 to 3 painters stretches the deadline from 12 to 20 days, keeping the painters×days product at 60.

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 whether to use inverse instead of direct rule of three?

Use inverse when increasing one quantity proportionally decreases the other, like speed and time or workers and deadline; if both grow together, like price and quantity, it is direct, and the formula switches from A×B=C×X to A/B=C/X.

Does inverse rule of three work the same for any number of workers or machines?

Only while the work stays perfectly divisible with no dependency between steps; dropping from 5 to 3 painters stretches the deadline from 12 to 20 days, but sequential tasks, where one step requires the previous one finished, do not follow that same proportion.

Why does the product of the two quantities need to stay equal on both sides of the equation?

Because it represents the fixed physical quantity behind the proportion, like a trip's distance or a tank's volume; in the taps example, the taps×hours product stays at 30 both for 3 taps in 10 h and for 5 taps in 6 h.

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inverse rule of three

Inverse Rule of Three

How the inverse proportion works

For a fixed distance, the higher the speed, the lower the time spent, and the product speed × time always equals that distance. Driving at 80 km/h for 3 h covers 240 km (80×3); keeping that same distance but at 100 km/h, the time drops to X=(80×3)/100=2.4 h, that is, 2 h 24 min, because speed rose 25% and time fell by the matching inverse ratio.

The same logic applies to flow rate: a tank that 3 taps fill in 10 hours has a constant product of 30 (taps × hours). With 5 taps running at once, the time drops to X=30/5=6 hours: raising the number of taps by 67% (from 3 to 5) does not cut the time in half, it shrinks by the exact ratio 5/3, from 10 h to 6 h.

Inverse proportion assumes each extra unit contributes identically to the others, with no coordination overhead: 5 painters finish a job in 12 days, and the product painters × days sits at 60; with only 3 painters, the deadline stretches to X=60/3=20 days. That prediction only holds exactly when the work is perfectly divisible among people; tasks with sequential steps, where one can only start after the previous finishes, do not follow the same proportion no matter how many people are added.

Examples

Speed × time (fixed distance)

Input: A=80, B=3, C=100
Expected output: X = 2.4

At 80 km/h for 3 h the trip covers 240 km; over the same distance at 100 km/h, the time drops to 2.4 h (2 h 24 min).

Taps filling a tank

Input: A=3, B=10, C=5
Expected output: X = 6

3 taps take 10 h; 5 taps keep the product at 30 and finish in 6 h, not by coincidence: 30÷5=6.

Painters finishing a job

Input: A=5, B=12, C=3
Expected output: X = 20

Dropping from 5 to 3 painters stretches the deadline from 12 to 20 days, keeping the painters×days product at 60.

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