Double the sides, quadruple the area: triangle scaling explained
Lengths and areas do not scale in the same way. Confusing them can lead to large errors when resizing a pattern or estimating coverage.
Triangle calculator →Compare a pair of similar triangles
A triangle with sides 3, 4 and 5 has perimeter 12 and area 6. Doubling every side gives 6, 8 and 10: the perimeter becomes 24, but the area becomes 24. The length multiplier is 2, while the area multiplier is 2² = 4. Enter both sets in the triangle tool to see the different changes side by side.
Generalize the multiplier
When every length is multiplied by a positive factor k, perimeter multiplies by k and area by k². A 150% print scale means k = 1.5, so the area is 2.25 times the original. If you want exactly twice the area while keeping the same shape, multiply every side by √2, approximately 1.4142, rather than by 2.
Scaling requires the same shape
Changing only one side generally changes the angles, so the square-factor rule no longer follows from that one length. Use all three actual new lengths to recalculate. Also distinguish drawing dimensions from real dimensions: a 1:100 linear scale corresponds to a 1:10,000 area scale. Convert measured drawing lengths before entering them when you want real-world area, and keep the resulting square units explicit.
Try the calculators
- Triangle calculator
Calculate area and perimeter from three sides.
- Rectangle area
Calculate a rectangle’s area and perimeter.
- Scientific calculator
Arithmetic, powers, trigonometry and logarithms.