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Triangle Calculator

Use the Triangle Calculator to solve sides, angles, perimeter, and area. Choose a method (SSS, SAS, ASA, AAS, or Base & Height) and fill only the fields required for that method.

Guidance: SSS requires a, b, c. SAS requires a, b, and the included angle C. ASA requires side a and angles B and C. AAS requires side a and angles A and B. Base & Height computes area only.

Angles are in degrees. The calculator validates triangle inequality and angle sums automatically.

The Triangle Calculator is a fast, accurate tool that lets you solve a triangle from common input combinations: three sides (SSS), two sides and the included angle (SAS), one side and two angles (ASA/AAS), or base and height for area. Whether you are a student, engineer, architect, or maker, this calculator streamlines geometry so you can focus on results.

What you can compute with the Triangle Calculator

Depending on what you know, the Triangle Calculator determines missing sides and angles, perimeter, area, and helpful derived measures such as altitudes (heights), inradius, and circumradius. It supports unit selection (mm, cm, m, in, ft) and lets you set decimal precision for crisp, readable output.

  • SSS: Enter three sides to get all angles, perimeter, and area.
  • SAS: Enter two sides and the included angle to solve the third side and remaining angles.
  • ASA/AAS: Enter one side and two angles to compute the other sides and complete the triangle.
  • Base & Height: Quickly compute area when you know the base and the corresponding height.

How to use the Triangle Calculator effectively

  1. Select your method: SSS, SAS, ASA, AAS, or Base & Height.
  2. Fill the required fields for the selected method. Only those inputs are needed.
  3. Choose your length units and desired decimal precision.
  4. Click Calculate to view results instantly.

For the most accurate results, keep inputs consistent: use the same length unit for all sides and ensure angles are in degrees. The calculator verifies triangle inequality (SSS) and ensures angle sums make sense (ASA/AAS), alerting you if values are inconsistent.

Formulas used by the Triangle Calculator

Behind the scenes, the calculator applies classical trigonometry:

  • Law of Cosines (SSS/SAS): c^2 = a^2 + b^2 ? 2ab cos(C)
  • Law of Sines (SAS/ASA/AAS): a/sin(A) = b/sin(B) = c/sin(C)
  • Heron's Formula (SSS area): A = \u221A[s(s?a)(s?b)(s?c)], where s is the semiperimeter
  • Area by angle: A = 1/2 ab sin(C)
  • Area by base and height: A = 1/2 bh

These equations are robust for all non-degenerate triangles and are carefully implemented to avoid rounding errors where possible.

Common use cases

Students often use the Triangle Calculator to check homework or experiment with geometric relationships. Engineers and builders can validate field measurements and infer missing dimensions. Makers and DIY enthusiasts benefit when laying out cuts, braces, or panels. In navigation and surveying, triangles are the backbone of triangulation and bearing calculations, making a reliable solver indispensable.

Pro tips for accurate triangle solving

  • When using SAS, ensure the angle you enter is included between the two known sides. The wrong angle yields the wrong third side.
  • For ASA/AAS, the sum of angles must be less than 180°; the calculator will compute the third angle automatically.
  • Use consistent units for all sides. The unit selector affects how results are labeled, including squaring for areas.
  • Increase decimal precision if you need more exact values for fabrication or analysis.

Why this Triangle Calculator stands out

Beyond raw computations, this tool presents results clearly: sides and angles, perimeter and area, plus derived measures like altitudes and radii. It balances rigor with usability, making it an ideal companion from the classroom to the jobsite. Try different input sets to see how changes ripple through a triangle's geometry and build intuition along the way.

FAQs

How do I use the Triangle Calculator for SSS inputs?

Choose SSS and enter all three sides (a, b, c). The Triangle Calculator will find all angles, perimeter, and area.

Which angle should I enter for SAS in the Triangle Calculator?

For SAS, enter the included angle C between sides a and b. The calculator then solves side c and the remaining angles.

Can the Triangle Calculator compute area from base and height only?

Yes. Select Base & Height, enter base and height, and it will output area without needing sides or angles.

Does the Triangle Calculator check triangle validity?

Yes. It enforces triangle inequality for SSS and validates angle sums for ASA/AAS to prevent impossible triangles.

What units does the Triangle Calculator support?

You can select mm, cm, m, in, or ft. Results are labeled with the chosen unit, with area shown in unit².

Can the Triangle Calculator handle decimal inputs?

Absolutely. Enter decimals for sides and angles, and set the desired decimal precision from 0 to 6.

What outputs does the Triangle Calculator provide?

It returns sides, angles, perimeter, area, and derived values like altitudes, inradius, and circumradius.

Is the Triangle Calculator suitable for ambiguous SSA cases?

SSA is not offered because it can be ambiguous. Use SAS, ASA, AAS, or SSS to ensure a unique solution.