Proportional Size Calculator
Choose direct or inverse proportion, enter a known pair of values and the new x. The calculator finds the constant of proportionality k, the new y, and how much each value changed, with a graph.
- Direct proportion
- Inverse proportion
- Constant k
Pick inverse when one value goes down as the other goes up, with their product staying the same.
Some things rise together, others move in opposite ways. In direct proportion y = kx, so doubling x doubles y. In inverse proportion y = k ÷ x, so doubling x halves y. If 4 workers take 6 days, then k = 24 and 8 workers take 3 days.
Direct and inverse examples
Everyday cases. Search for an example.
| Example | Type | Known | New |
|---|---|---|---|
| Hours and pay | Direct | 10 h, 150 | 20 h, 300 |
| Workers and days | Inverse | 4 workers, 6 days | 8 workers, 3 days |
| Speed and time | Inverse | 60 km/h, 2 h | 40 km/h, 3 h |
| Weight and cost | Direct | 2 kg, 7 | 5 kg, 17.50 |
| Gear teeth and speed | Inverse | 20 teeth, 300 rpm | 40 teeth, 150 rpm |
| Distance and fuel | Direct | 100 km, 6 L | 250 km, 15 L |
k is worked from the known pair.
x and y
Inverse, k = 24. Slide x.
The curve shows y = 24 ÷ x and the new point moving along it.
How to work out proportion
Find k first. Step through it.
Pick the type
Direct or inverse.
Plot a few points if unsure. Direct gives a straight line through zero, inverse a curve.
Direct or inverse
Two kinds. Compare them.
Rise together.
Move apart.
No fixed rule.
Many real cases are only roughly proportional, so treat answers as estimates.
Before you solve
Proportion checks. Tick each item.
Tick each item as you go.
Fixed costs, such as a call-out fee, break direct proportion.
What you get
Proportional change. Each tile explains one result.
New value.
Constant.
Used.
Factor.
Factor.
The constant k carries the units, such as pay per hour or worker-days.
Frequently Asked Questions
No question matches that search.
What does directly proportional mean?
Two values rise or fall together at the same rate, so y equals k times x.
What does inversely proportional mean?
As one value rises the other falls, so that their product stays the same.
How do I find the constant of proportionality?
For direct proportion divide y by x. For inverse proportion multiply x by y.
Is speed and time inverse proportion?
Yes, for a fixed distance. Faster means less time.
What does a direct proportion graph look like?
A straight line through the origin.
What does an inverse proportion graph look like?
A curve that gets closer to both axes but never touches them.
How do I tell which type it is?
Ask whether doubling one value doubles or halves the other.
See how things change together
Find k from one known pair and you can predict any other value, whether the two move together or apart.
More size calculators
Each one has its own calculator, worked examples and answers to common questions.