Similar Triangle Calculator: Missing Side & Scale Factor

 

Find a missing side in two triangles that are already known to be similar. Enter two sides from Triangle 1 and the side in Triangle 2 corresponding to the first one. All lengths must use the same unit.

Triangle 1 side aTriangle 1 side bTriangle 2 side A (corresponds to a)

The missing side B corresponds to side b. Match sides using equal opposite angles or the stated vertex correspondence, not just how a drawing is rotated. This calculator assumes similarity; it cannot prove it from these three entries.

JavaScript is required for interactive calculations. Formulas and examples remain available below.

How to find a missing side in similar triangles

Similar triangles have equal corresponding angles and proportional corresponding sides. If side a corresponds to side A, the scale factor from Triangle 1 to Triangle 2 is k = A / a. A second corresponding side follows B = b x k, or B = b x A / a.

Keep the direction consistent. A/a describes Triangle 1 to Triangle 2; a/A describes the reverse. Multiplying by the reverse factor when you need the forward one gives the wrong side length.

Worked example

Enter Triangle 1 side a 3, Triangle 1 side b 5 and Triangle 2 side A (corresponds to a) 6. Select Calculate missing side. The scale factor is 6 / 3 = 2, so Triangle 2 side B is 5 x 2 = 10.

The reverse scale factor is 0.5. The perimeter multiplier is 2 and the area multiplier is 4. These relationships apply only if the triangles really are similar and the side pairing is correct.

Enlargement, reduction and equal size

A forward scale factor greater than one describes an enlargement. A factor between zero and one describes a reduction. A factor of one gives equal corresponding side lengths. Positive side lengths are required; zero or negative values do not describe triangle sides.

For a reduction, let a = 8, b = 12 and A = 2. The scale factor is 0.25, giving B = 3. The perimeter multiplier is 0.25, while the area multiplier is 0.0625. The area shrinks by the square of the side multiplier.

Why perimeter and area scale differently

Every corresponding length in similar triangles is multiplied by k. Their perimeters therefore also differ by k. Areas combine two length dimensions and differ by k squared. A side multiplier of three gives a perimeter multiplier of three and an area multiplier of nine.

The calculator reports these multipliers without inventing actual areas or perimeters. Two supplied sides alone do not determine an arbitrary triangle's area, and the third side has not been entered.

Confirm similarity and correspondence first

Common ways to establish triangle similarity include two equal corresponding angles, three proportional corresponding sides, or two proportional side pairs with equal included angles. A matching-looking sketch is not proof. Use the information given in the problem and label corresponding vertices carefully.

This tool does not check angle conditions, solve an arbitrary triangle or certify that the inputs describe a particular drawing. If you know you have a right triangle and need a missing side or angle, use the Right Triangle Calculator.

For a step-by-step walkthrough, read How to Find Missing Sides in Similar Triangles.

Units, precision and privacy

Convert all entries to one common unit before calculating. A value entered in centimeters cannot be mixed directly with a corresponding value in meters. Each input must be greater than zero up to 1000000000. Results display up to six decimal places, with scientific notation for very small or large values.

Calculations use floating-point arithmetic and run locally in your browser. The calculator does not save or transmit your measurements. The hosting website may use separate analytics or advertising services.