Calculator Inputs
Formula Used
Perimeter: P = a + b + c
Semiperimeter: s = (a + b + c) / 2
Area by Heron's Formula: K = √[s(s-a)(s-b)(s-c)]
Angles by Law of Cosines: A = cos⁻¹((b² + c² - a²) / 2bc)
SAS missing side: c² = a² + b² - 2ab cos(C)
ASA/AAS sides: a / sin(A) = b / sin(B) = c / sin(C)
Height: h = 2K / base
Inradius: r = K / s
Circumradius: R = abc / 4K
Median: mₐ = ½√(2b² + 2c² - a²)
How to Use This Calculator
- Select the known triangle case from the method menu.
- Use SSS when all three side lengths are known.
- Use SAS when two sides and their included angle are known.
- Use ASA/AAS when two angles and one side are known.
- Enter a unit label, such as cm, m, inch, or feet.
- Choose the decimal precision for the final values.
- Press the calculate button to view results above the form.
- Use the CSV or PDF button to save the result.
Example Data Table
| Case | Known Values | Expected Output | Best Method |
|---|---|---|---|
| Standard triangle | a = 7, b = 8, c = 9 | Area, perimeter, angles, radii | SSS |
| Two sides with angle | a = 12, b = 15, C = 40° | Missing side and all measures | SAS |
| Survey triangle | A = 45°, B = 65°, side a = 20 | Remaining sides and angle C | ASA/AAS |
| Right style check | a = 3, b = 4, c = 5 | Right triangle classification | SSS |
Understanding Triangle Measures
Why Triangle Measures Matter
A triangle looks simple, yet it stores many useful measurements. Each side, angle, height, radius, and median tells a different story. These values help in geometry, design, surveying, construction, mapping, and physics. A triangle calculator saves time because it links these values through trusted rules. You can enter the measures you already know. Then the tool solves the hidden parts.
Choosing the Right Input Case
The most direct case is SSS. It needs three valid sides. The calculator first checks the triangle inequality. This prevents impossible shapes. SAS is useful when two sides and their included angle are known. It uses the law of cosines to find the third side. ASA and AAS are useful when angles guide the shape. They use the law of sines to scale every side.
Area and Perimeter
Area shows the space covered by the triangle. Perimeter shows the total boundary length. Heron's formula is powerful because it needs only side lengths. After any method finds all sides, the calculator can use Heron's formula. It also finds the semiperimeter, which is half of the perimeter. This value appears in several triangle formulas.
Advanced Measures
Heights measure the shortest distance from a vertex to the opposite side. Medians connect a vertex to the midpoint of the opposite side. The inradius belongs to the circle that fits inside the triangle. The circumradius belongs to the circle passing through all three vertices. Angle bisectors divide angles into two equal parts. These measures support deeper analysis.
Reading the Result
The result table gives clean values with the selected unit. The plot shows the triangle shape using computed coordinates. The classification shows whether the triangle is scalene, isosceles, or equilateral. It also checks if the triangle is acute, right, or obtuse. Use the export buttons when you need a record for study, reports, worksheets, or project notes.
FAQs
1. What does this triangle calculator measure?
It measures sides, angles, area, perimeter, semiperimeter, heights, medians, inradius, circumradius, and angle bisectors. It also classifies the triangle by sides and angles.
2. Which input method should I choose?
Choose SSS for three sides. Choose SAS for two sides and their included angle. Choose ASA/AAS for two angles and one known side.
3. Why do I get an invalid triangle error?
The side lengths may break the triangle inequality rule. Any two sides must have a sum greater than the third side.
4. Does the calculator support angle degrees?
Yes. All angle inputs use degrees. The calculator converts degrees internally when trigonometric formulas are needed.
5. What is Heron's formula used for?
Heron's formula finds triangle area from three side lengths. It is useful after SSS, SAS, or ASA/AAS finds all sides.
6. What is the inradius?
The inradius is the radius of the circle that fits inside the triangle and touches all three sides.
7. What is the circumradius?
The circumradius is the radius of the circle that passes through all three vertices of the triangle.
8. Can I download the results?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a clean printable summary.