What is the Triangle Ratio Calculator?
This tool turns a side ratio such as 3 : 4 : 5 into real measurements. Give it the three ratio terms plus the actual length of any one side, and it computes the other two sides and the perimeter using simple proportional scaling. It works for any triangle whose sides share a known proportion — useful in geometry homework, drafting, model building, and scaling drawings up or down.
How to use it
Enter the ratio terms a, b and c. Choose which side you actually know, then type that side's length. The calculator finds a single "scale unit" — the real length represented by one ratio term — and multiplies every term by it.
The formula explained
If the ratio is a : b : c and you know side k with length L, the scale unit is \(u = L / r_{k}\). Then each side is \(\text{side}_{i} = r_{i} \times u\). This preserves the proportion exactly, so the resulting triangle is similar to one drawn from the bare ratio.
Worked example
Ratio 3 : 4 : 5, and side a = 6. The scale unit is $$6 \div 3 = 2.$$ So side a = \(3 \times 2 = 6\), side b = \(4 \times 2 = 8\), side c = \(5 \times 2 = 10\), and the perimeter is $$6 + 8 + 10 = 24.$$
FAQ
Does it check that a triangle is valid? No — it only scales the ratio. For a valid triangle the two shorter sides must sum to more than the longest side.
Can I use decimals in the ratio? Yes, any positive numbers work, e.g. 1.5 : 2 : 2.5.
What units does it use? Whatever unit you enter the known length in — the answers come out in the same unit.
