BBuildculate
measurement

Triangle Calculator

Solve right-angled and oblique triangles. Calculate unknown sides, angles, area, perimeter, altitudes, and radii using SSS, SAS, ASA, AAS, and right triangle methods.

CalculatorHow to CalculateFormulas & ExamplesFAQs

Solve unknown dimensions, angles, area, and heights.

Dimension Specifications

Dimension Guide
Side ASide BSide C

Ready to Solve

Select a solve method, enter your dimensions, and click Calculate to solve the triangle.

Formula Details

Select a solve method in the calculator above to display its specific formula, or browse the equations below:

Calculation Example

Worked Example
Scenario

Roof Truss Design (SSS): A carpenter is designing a triangular roof truss. The bottom cord (Side C) is 24 feet, the left rafter (Side A) is 14 feet, and the right rafter (Side B) is 14 feet. Determine the roof pitch angles at the eaves.

Calculation Steps
  1. 1.Select the SSS (Three Sides) method and Imperial units (ft).
    Side A = 14 ft, Side B = 14 ft, Side C = 24 ft
  2. 2.Compute internal Angle A (pitch at left eave) using the Law of Cosines.
    A = acos((14² + 24² - 14²) / (2 × 14 × 24)) = acos(576 / 672) = 31.00°
  3. 3.Because the truss is isosceles (Side A = Side B), Angle B equals Angle A.
    Angle B = 31.00° | Angle C (peak angle) = 180° - 31° - 31° = 118.00°
  4. 4.Determine the heights (altitude) and surface area.
    Area = 95.12 ft² | Semiperimeter = 26.00 ft | Peak Height (h_c) = 7.94 ft
Final Quantity NeededAngles: A = 31.00°, B = 31.00°, C = 118.00° | Peak Height: 7.94 ft | Area: 95.12 ft²
Worked Example
Scenario

Site Triangulation Survey (ASA): A surveyor measures a triangular property boundary. They stand at two corners and measure the distance between them as 150 meters. The internal angle at the first corner is 55°, and at the second is 65°. Find the other boundary lengths.

Calculation Steps
  1. 1.Select the ASA (Two Angles & Included Side) method and Metric units (m).
    Angle A = 55°, Angle B = 65°, Side C = 150 m
  2. 2.Compute the third angle opposite to the measured baseline.
    Angle C = 180° - 55° - 65° = 60.00°
  3. 3.Use the Law of Sines to solve for Side A and Side B.
    Side A = 150 × sin(55°) / sin(60°) = 141.88 m | Side B = 150 × sin(65°) / sin(60°) = 156.96 m
  4. 4.Calculate the total plot area and boundary perimeter.
    Area = 9,639.73 m² | Perimeter = 448.84 m
Final Quantity NeededSide A: 141.88 m, Side B: 156.96 m | Total Perimeter: 448.84 m | Area: 9,639.73 m²
Worked Example
Scenario

Property Boundary Offset (SAS): A designer needs to find the diagonal boundary fence distance between two points. Point A is 45 yards from the corner junction, Point B is 60 yards, and the angle between the two boundary lines is 75°.

Calculation Steps
  1. 1.Select the SAS (Two Sides & Angle) method and select yards (yd) as units.
    Side A = 45 yd, Side B = 60 yd, Angle C = 75.00°
  2. 2.Solve for diagonal Side C using the Law of Cosines.
    Side C = √(45² + 60² - 2 × 45 × 60 × cos(75°)) = √(2025 + 3600 - 1397.62) = 65.02 yd
  3. 3.Compute remaining angles and structural area.
    Angle A = 41.86° | Angle B = 63.14° | Area = 1,304.00 yd²
Final Quantity NeededFence Diagonal (Side C): 65.02 yd | Angles: A = 41.86°, B = 63.14° | Area: 1,304.00 yd²

How to Use

Follow these simple steps to solve and classify any triangle configuration:

  1. Choose a Solve Method: Select from SSS, SAS, ASA, AAS, Right Triangle, or Base & Height options.
  2. Select Units: Set the preferred length unit system (Imperial vs Metric) and choose the appropriate angle unit (Degrees vs Radians) in the form header.
  3. Enter Known Values: Input your measured sides or angles into the dynamic fields. For Right Triangles, provide exactly two values (Angle C is automatically set to 90°).
  4. Click Calculate: Click the Calculate button to solve the unknown side lengths, angles, height altitudes, and area.
  5. Review Results: Examine the classification card, side-by-side values, inradius/circumradius measurements, and equivalent system conversions.
  6. Reset: Click Reset at any time to clear the inputs and start a new calculation.

Frequently Asked Questions

What is the Law of Sines?
The Law of Sines is a geometric rule stating that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). It is particularly useful for solving triangles when you know two angles and one side (ASA or AAS).
What is the Law of Cosines?
The Law of Cosines relates the three sides of a triangle to the cosine of one of its angles: c² = a² + b² - 2ab cos(C). This formula functions like an extension of the Pythagorean Theorem for oblique triangles and is used when solving SSS (Three Sides) or SAS (Two Sides & Angle) configurations.
How do I know which solve method to select?
Choose the method based on the dimensions you have measured: SSS if you have all three side lengths; SAS if you have two sides and the angle between them; ASA if you have two angles and the side between them; AAS if you have two angles and a side opposite one of them; Right Triangle if you are working with a 90° corner and know two other properties; or Base & Height if you simply need the area.
Why is the calculator telling me my triangle is invalid?
A triangle is invalid if the inputs violate basic geometry laws: (1) The Triangle Inequality Theorem requires the sum of any two sides to be strictly greater than the third side (e.g. side lengths of 2, 2, and 5 cannot form a triangle). (2) The sum of internal angles must be strictly less than 180° (or π radians) when entering two angles (ASA or AAS).
Can I switch between degrees and radians?
Yes. Toggle the degrees/radians button in the header of the calculator card. The input placeholders and active values will automatically update, and calculations will translate. Degrees are standard in framing and roofing, whereas Radians are common in civil surveying computations.
How accurate are the geometric results?
Calculations are conducted using double-precision floating-point numbers in TypeScript. Altitudes, semiperimeter, inradius, circumradius, and area calculations conform to standard analytical equations. While highly precise, structural framing cuts should always be verified on-site before cutting expensive timber.

Need to calculate structural dimensions, volumes, or stair layouts?

Estimate stair riser heights, roof shingle counts, trench cut volumes, aggregate weights, and concrete budgets with precise construction guidelines.

View CategoriesAbout Buildculate

Recommended Calculators

Similar Tools
measurementActive

Area Calculator

Calculate area of squares, rectangles, circles, and irregular shapes.

Open Calculator
measurementActive

Volume Calculator

Estimate volume of prisms, cylinders, spheres, and custom shapes.

Open Calculator
measurementActive

Slope Calculator

Determine slope percent, angle, drop heights, and pitch configurations.

Open Calculator
measurementActive

Stair Calculator

Calculate stair riser heights, tread widths, stringer lengths, and run angles.

Open Calculator
materialActive

Concrete Calculator

Calculate concrete volume, weight, and bag quantities for common construction shapes.

Open Calculator
Disclaimer

Calculations are estimates based on the values you enter and standard engineering formulas. Results are intended for planning and estimation only. Always verify critical measurements, specifications, and local building requirements before purchasing materials or beginning construction.