Special Right Triangles Calculator
Calculate special right triangles instantly in your browser.
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What this tool does
Calculate special right triangles instantly in your browser. These exact ratios come from splitting a square (45-45-90) or an equilateral triangle (30-60-90) in half — no trig is needed.
How to use the Special Right Triangles Calculator
- Enter or select triangle type.
- Enter or select known side.
- Enter or select length of the known side.
- Read the calculated result; change any measurement to compare alternatives.
Formula
45-45-90 triangles have sides in the ratio 1 : 1 : √2. 30-60-90 triangles have sides in the ratio 1 : √3 : 2 (short leg opposite 30°, long leg opposite 60°, hypotenuse double the short leg).
- type
- Triangle type
- known
- Known side
- value
- Length of the known side
These exact ratios come from splitting a square (45-45-90) or an equilateral triangle (30-60-90) in half — no trig is needed.
Worked example
For special right triangles calculator, the following measurements illustrate the exact method: Triangle type: 45; Known side: leg; Length of the known side: 5.
Inputs
- Triangle type45-45-90
- Known sideLeg (45°) / short leg (30°)
- Length of the known side5
Result
- Leg (both legs are equal)5
- Hypotenuse7.07
- Area12.5
- Perimeter17.07
- Ratio check (leg : leg : hyp)1 : 1 : 1.41421356237
Results explained
- Leg (both legs are equal)
- Leg (both legs are equal) from the formula above. These exact ratios come from splitting a square (45-45-90) or an equilateral triangle (30-60-90) in half — no trig is needed.
- Hypotenuse
- Hypotenuse from the formula above. These exact ratios come from splitting a square (45-45-90) or an equilateral triangle (30-60-90) in half — no trig is needed.
- Area
- Area from the formula above. These exact ratios come from splitting a square (45-45-90) or an equilateral triangle (30-60-90) in half — no trig is needed.
- Perimeter
- Perimeter from the formula above. These exact ratios come from splitting a square (45-45-90) or an equilateral triangle (30-60-90) in half — no trig is needed.
- Ratio check (leg : leg : hyp)
- Ratio check (leg : leg : hyp) from the formula above. These exact ratios come from splitting a square (45-45-90) or an equilateral triangle (30-60-90) in half — no trig is needed.
Frequently asked questions
45-45-90 triangles have sides in the ratio 1 : 1 : √2. 30-60-90 triangles have sides in the ratio 1 : √3 : 2 (short leg opposite 30°, long leg opposite 60°, hypotenuse double the short leg).
These exact ratios come from splitting a square (45-45-90) or an equilateral triangle (30-60-90) in half — no trig is needed.
Where mathematically meaningful, yes. Fields specify permitted ranges and undefined operations display an error.
Exact integer calculations use safe integers; decimal calculations use browser floating point, so small rounding differences can occur.
All values remain in your browser and are never uploaded.