Triangle Leg Calculator
A Triangle Leg Calculator helps you compute a missing side (leg) or the hypotenuse of a right triangle. Whether you’re solving geometry homework, designing a ramp, or checking measurements on a build, this simple tool uses the Pythagorean theorem to give instant, accurate results.
🔹 When to Use a Triangle Leg Calculator
Use it when you know any two of these values for a right triangle:
- Both legs (find hypotenuse)
- One leg and the hypotenuse (find the other leg)
It only works for right triangles — triangles with a 90° angle.
🔹 Key Formula (Pythagorean theorem)
For a right triangle with legs aaa and bbb and hypotenuse ccc: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2
Solve for the missing side:
- To find the hypotenuse ccc:
c=a2+b2c = \sqrt{a^2 + b^2}c=a2+b2
- To find a missing leg aaa (when bbb and ccc known):
a=c2−b2a = \sqrt{c^2 – b^2}a=c2−b2
(Ensure c>bc > bc>b before using the second formula; otherwise the inputs are invalid.)
🔹 Worked Examples
Example 1 — Find the hypotenuse
Legs: a=3a = 3a=3, b=4b = 4b=4 c=32+42=9+16=25=5c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5c=32+42=9+16=25=5
Example 2 — Find a missing leg
Hypotenuse c=13c = 13c=13, known leg b=5b = 5b=5 a=132−52=169−25=144=12a = \sqrt{13^2 – 5^2} = \sqrt{169 – 25} = \sqrt{144} = 12a=132−52=169−25=144=12
Example 3 — Decimal values
Hypotenuse c=10c = 10c=10, leg b=6.4b = 6.4b=6.4 a=102−6.42=100−40.96=59.04≈7.684a = \sqrt{10^2 – 6.4^2} = \sqrt{100 – 40.96} = \sqrt{59.04} \approx 7.684a=102−6.42=100−40.96=59.04≈7.684
🔹 Special Triangles (quick shortcuts)
- 3–4–5 triangle family (scale multiples) — useful for construction squaring.
- 30°–60°–90° triangle: if short leg =x= x=x, long leg =x3= x\sqrt{3}=x3, hypotenuse =2x= 2x=2x.
- 45°–45°–90° triangle (isosceles right): legs equal; hypotenuse =leg×2= leg \times \sqrt{2}=leg×2.
🔹 Tips & Best Practices
- Units matter — keep units consistent (all in meters, feet, inches, etc.).
- Validate inputs — if calculating a leg from hypotenuse, ensure hypotenuse > known leg.
- Round reasonably — for construction, round to the nearest practical unit (e.g., 1/16″ or mm).
- Check for impossible inputs — negative values or c≤bc \le bc≤b are invalid for right triangles.
🔹 Common Uses
- School geometry/homework help
- Carpentry & framing (squaring corners)
- Roof pitch & ramp calculations
- Engineering and CAD quick checks
🔹 FAQs
Q: Can this calculator find angles?
A: Not directly — it finds sides. To get angles, use trigonometry (e.g., sinθ=opposite/hypotenuse\sin\theta = opposite/hypotenusesinθ=opposite/hypotenuse, cosθ=adjacent/hypotenuse\cos\theta = adjacent/hypotenusecosθ=adjacent/hypotenuse) once sides are known.
Q: What if my triangle is not right-angled?
A: Use the Law of Cosines for non-right triangles: c2=a2+b2−2abcos(C)c^2 = a^2 + b^2 – 2ab\cos(C)c2=a2+b2−2abcos(C)
Q: Will rounding introduce large errors?
A: For precise engineering work, keep more decimal places during calculation and round only the final result to the needed precision.