Side Side Side Triangle Calculator

Enter three sides and solve every key triangle measure. Review formulas, classifications, examples, and exports. Create accurate SSS geometry reports in seconds today easily.

Calculator Inputs

Formula Used

Triangle validity: a + b > c, a + c > b, and b + c > a.

Semiperimeter: s = (a + b + c) / 2

Area: A = √[s(s - a)(s - b)(s - c)]

Perimeter: P = a + b + c

Angle A: cos(A) = (b² + c² - a²) / 2bc

Angle B: cos(B) = (a² + c² - b²) / 2ac

Angle C: C = 180° - A - B

Height: h = 2A / side

Median: ma = ½√(2b² + 2c² - a²)

Inradius: r = A / s

Circumradius: R = abc / 4A

How to Use This Calculator

  1. Enter the three known side lengths.
  2. Use the same unit for every side.
  3. Add a unit label, such as cm, m, in, or ft.
  4. Select the decimal precision for your report.
  5. Press the calculate button.
  6. Review angles, area, perimeter, radii, heights, and medians.
  7. Download the result as CSV or PDF when needed.

Example Data Table

Side a Side b Side c Triangle Type Expected Area
3 4 5 Scalene right 6
5 5 6 Isosceles acute 12
6 6 6 Equilateral acute 15.5885
7 8 9 Scalene acute 26.8328

About This Side Side Side Calculator

A side side side triangle calculator starts with three known lengths. It then solves the entire triangle from those sides. This method is useful when no angle is given. Surveying, drafting, navigation, roofing, and classroom problems often use it.

The tool first checks whether the three sides can form a triangle. Two shorter sides must be greater than the longest side. If that rule fails, the shape is not possible. This prevents false area and angle values.

After validation, the calculator finds the semiperimeter. It uses Heron's formula to calculate area. Then it applies the law of cosines for each angle. These angles show whether the triangle is acute, right, or obtuse. The result also labels the triangle as scalene, isosceles, or equilateral.

Advanced Measurements

Advanced measurements give more context. The perimeter shows total boundary length. The inradius describes the circle touching all three sides. The circumradius describes the circle through every vertex. Altitudes show perpendicular height from each side. Medians show lines from vertices to opposite side midpoints.

Use decimal precision to match your project. A higher precision is useful for engineering checks. A lower precision is easier for worksheets and reports. The unit label is optional. It can represent inches, feet, meters, or any consistent unit.

Export and Accuracy

The calculator also supports record keeping. You can download a CSV file for spreadsheets. You can create a PDF summary for sharing. Both options help keep calculations traceable.

For best results, measure each side carefully. Use the same unit for every input. Avoid mixing feet and inches without conversion. Small measurement errors can change angles. Very flat triangles are especially sensitive.

Complete outputs reduce repeated work. Instead of solving one value at a time, you receive a complete set. That makes comparison easier during design checks. It also helps students see how formulas connect. Area, angles, radii, heights, and medians all come from the same three sides. The example table shows typical inputs. Use it to test your own results before entering data.

This calculator is a general geometry tool. It does not replace licensed design review. For construction or structural work, verify local rules. Still, it gives a fast and transparent way to review SSS triangle geometry.

FAQs

What is a side side side triangle?

It is a triangle problem where all three side lengths are known. The calculator uses those sides to find angles, area, perimeter, heights, medians, and radius values.

Can any three sides make a triangle?

No. The sum of any two sides must be greater than the third side. The calculator checks this before solving the triangle.

Which formula finds the area?

The calculator uses Heron's formula. It first finds the semiperimeter, then applies the square root formula using all three side lengths.

How are the angles calculated?

The calculator uses the law of cosines. Each angle is solved from the three known sides, then shown in degrees.

Can I use different units?

Use any unit, but keep it consistent. Do not mix inches, feet, meters, or centimeters unless you convert them first.

What does the inradius mean?

The inradius is the radius of the circle that touches all three triangle sides from inside the triangle.

What does the circumradius mean?

The circumradius is the radius of the circle passing through all three vertices of the triangle.

Can I export the results?

Yes. After calculation, use the CSV button for spreadsheet data or the PDF button for a simple printable report.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.