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Triangle Calculator

Calculate triangle properties

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Last Updated: March 2, 2026
avatarBy Viblaa Team

All angles

Area and perimeter

Triangle type identification

You know two sides of a triangle and the angle between them—what's the area? You have three sides—what are the angles? The surveyor measured two angles and one side—what are the other measurements?

Triangle calculations go beyond the Pythagorean theorem. This calculator handles any triangle—right, acute, or obtuse—using trigonometry to find sides, angles, and area.

What is Triangle Calculation?

Triangle calculations use trigonometric relationships to find unknown sides, angles, and area from known values. Different formulas apply depending on what information you have: SSS, SAS, ASA, or AAS.

Key formulas:

Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines:
c² = a² + b² - 2ab¡cos(C)

Area formulas:
A = ½ × base × height
A = ½ × a × b × sin(C) (SAS)
A = √[s(s-a)(s-b)(s-c)] (Heron's, where s = (a+b+c)/2)
Sum of Angles = 180°

Triangle angles always sum to 180°. If you know two angles, the third is: 180° - angle1 - angle2.

Why People Actually Need This Tool

Not All Triangles Are Right

The Pythagorean theorem only works for right triangles. Real-world triangles are often oblique—these need the law of sines and cosines.

  1. Surveying — Calculate distances and areas from angle measurements.

  2. Navigation — Triangulation to determine position.

  3. Construction — Calculate roof angles and truss dimensions.

  4. Engineering — Analyze force triangles and structural geometry.

  5. Land measurement — Calculate irregular plot areas.

  6. Astronomy — Determine distances using parallax triangles.

  7. Woodworking — Calculate miter angles for non-90° joints.

How to Use the Triangle Calculator

  1. Select what you know — SSS, SAS, ASA, or AAS.

  2. Enter known values — Sides and/or angles.

  3. View results — All sides, angles, area, and perimeter.

GivenWhat You KnowMethod Used
SSSThree sidesLaw of cosines for angles
SASTwo sides and included angleLaw of cosines for side
ASATwo angles and included sideLaw of sines
AASTwo angles and non-included sideLaw of sines
SSATwo sides and non-included angleAmbiguous case
SSA Can Have Two Solutions

Given two sides and an angle not between them, there might be two valid triangles. This is the "ambiguous case."

Real-World Use Cases

1. The Roof Truss

Context: Roof span 30 feet, ridge 8 feet above attic floor.

Problem: What's the rafter length and roof angle?

Solution: Half span = 15 ft. Rafter = √(15² + 8²) = 17 ft. Angle = arctan(8/15) = 28.1°.

Outcome: Rafter length and cut angle determined.

2. The Property Survey

Context: Triangular lot with sides 100m, 120m, 80m.

Problem: What's the area?

Solution: s = (100+120+80)/2 = 150. A = √[150×50×30×70] = √15,750,000 = 3969 m².

Outcome: Lot area calculated using Heron's formula.

3. The Navigation Problem

Context: Two landmarks are 5 km apart. Angles to destination: 35° and 65° from each.

Problem: Distance to destination from each landmark?

Solution: Third angle = 180-35-65 = 80°. Use law of sines: distances are 4.35 km and 2.89 km.

Outcome: Position triangulated from known landmarks.

4. The Deck Corner

Context: Deck corner isn't 90°. Measured angle is 110°.

Problem: Need miter cut angles for railing.

Solution: External angle = 180° - 110° = 70°. Each miter = 70°/2 = 35°.

Outcome: Correct miter angles for non-square corner.

5. The Force Analysis

Context: Two forces: 100N at 30°, 150N at 90° from horizontal.

Problem: What's the resultant force?

Solution: Vector triangle with 60° included angle. R² = 100² + 150² - 2×100×150×cos(120°). R = 217.9N.

Outcome: Resultant force calculated for structural design.

6. The Shadow Problem

Context: 6-foot person casts 8-foot shadow. Sun angle?

Problem: Calculate sun elevation angle.

Solution: tan(θ) = 6/8 = 0.75. θ = 36.9°.

Outcome: Solar angle determined for sundial or solar panel.

7. The Irregular Garden

Context: Triangular garden plot. Measured: 2 sides (12m, 15m) and included angle (48°).

Problem: Area of garden?

Solution: A = ½ × 12 × 15 × sin(48°) = 66.9 m².

Outcome: Planting area calculated for irregular shape.

Common Mistakes and How to Avoid Them

Angle Mode Matters

Calculators use degrees or radians. 45° ≠ 45 radians. Most practical work uses degrees—verify your calculator mode.

Using Pythagorean on Oblique Triangles
❌ The Mistake
Applying a² + b² = c² to a triangle without a right angle.
✅ The Fix
Pythagorean theorem requires 90° angle. Use law of cosines for other triangles.
Wrong Angle in Cosine Formula
❌ The Mistake
Using any angle instead of the angle OPPOSITE the side you're solving for.
✅ The Fix
c² = a² + b² - 2ab¡cos(C) where C is opposite side c.
Ignoring Ambiguous Case
❌ The Mistake
Getting one answer for SSA problem when two triangles are possible.
✅ The Fix
SSA can have 0, 1, or 2 solutions. Check if supplementary angle also works.
Calculator in Radians Mode
❌ The Mistake
Entering 45 degrees but calculator interprets as 45 radians.
✅ The Fix
Check calculator mode. DEG for degrees, RAD for radians. Most problems use degrees.
Forgetting Angle Sum = 180°
❌ The Mistake
Getting three angles that don't add to 180° and not checking.
✅ The Fix
Always verify: angles must sum to exactly 180°. If not, you made an error.

Privacy and Data Handling

This Triangle Calculator operates entirely in your browser.

  • No calculations are sent to any server.
  • No measurements are stored.
  • No account required.
  • Works completely offline.

Your calculations stay private.

Conclusion

Triangle calculations extend beyond right angles to solve real-world geometry. Surveying, navigation, construction, and engineering all require working with oblique triangles.

This calculator handles any triangle configuration—enter what you know, get complete information about sides, angles, and area.

Three sides, three angles, infinite applications.

Frequently Asked Questions