Triangle Calculator
Enter the three sides of any triangle and get its three angles, the area, the perimeter, the inscribed and circumscribed circle radii.
Try your own numbers
Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
Open in the calculator with these values
About this calculator
This page calculates angle A, opposite side a, angle B, opposite side b, angle C, opposite side c and 4 more results from side a, side b and side c. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Use this to find the angles of a triangle you have measured with a tape, the area of a triangular plot or panel, or the angle between two cable runs from the three distances. For a right triangle with only two sides known use the Pythagorean theorem calculator.
Cross-check: 35 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Pure mathematics or statistics; no electrical standard governs the method |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 35 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Side a | 7 |
| Side b | 8 |
| Side c | 9 |
- s = (a + b + c) / 2 = 12
- Area = √(s (s − a)(s − b)(s − c)) = 26.83281573
- Angle A = 48.1896851° Angle B = 58.41186449° Angle C = 73.3984504°
- Perimeter = 24 Inscribed radius = 2.2360679775 Circumscribed radius = 4.6957427527
Assumptions
- The three sides must satisfy the triangle rule: each side is shorter than the sum of the other two. If the longest side equals the sum of the other two the triangle is flat and is rejected
- Angles come from the law of cosines and always add up to 180°
- The area is found with Heron's formula in a form that stays accurate for thin triangles
- The tool works on plain numbers and does not track units: enter all three sides in the same unit; the area is in that unit squared
- A warning is shown when the triangle is right-angled, as the Pythagorean theorem calculator then also applies
Use this to find the angles of a triangle you have measured with a tape, the area of a triangular plot or panel, or the angle between two cable runs from the three distances. For a right triangle with only two sides known use the Pythagorean theorem calculator.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Side a | (number) | 0 or more, up to 1,000,000,000,000 | Enter all three sides, in one consistent unit. The two shorter sides together must be longer than the longest. |
| Side b | (number) | 0 or more, up to 1,000,000,000,000 | |
| Side c | (number) | 0 or more, up to 1,000,000,000,000 |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Angle A, opposite side a (degrees) | (number) | Shown to 8 decimal places | |
| Angle B, opposite side b (degrees) | (number) | Shown to 8 decimal places | |
| Angle C, opposite side c (degrees) | (number) | Shown to 8 decimal places | |
| Area (Heron's formula) | (number) | Shown to 10 decimal places | |
| Perimeter | (number) | Shown to 10 decimal places | |
| Inscribed circle radius (area / s) | (number) | Shown to 10 decimal places | |
| Circumscribed circle radius (abc / 4 area) | (number) | Shown to 10 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with side a
| Side a | Angle A, opposite side a | Angle B, opposite side b | Angle C, opposite side c |
|---|---|---|---|
| 1.75 | 9.70896852 | 50.43859931 | 119.85243217 |
| 3.5 | 22.7982481 | 62.3359955 | 94.8657564 |
| 7 | 48.1896851 | 58.41186449 | 73.3984504 |
| 14 | 110.74237995 | 32.30254521 | 36.95507484 |
Other inputs are the same as in the worked example above.
Standards and further reading
Complex numbers, rectangular and polar form and angle conversion are standard mathematics, not the subject of a standard. Standards apply when the result feeds an electrical design, and they set the method there.
Frequently asked questions
What do I need to enter?
Enter side a, side b and side c. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
The three sides must satisfy the triangle rule: each side is shorter than the sum of the other two. If the longest side equals the sum of the other two the triangle is flat and is rejected. Angles come from the law of cosines and always add up to 180°. The area is found with Heron's formula in a form that stays accurate for thin triangles. The tool works on plain numbers and does not track units: enter all three sides in the same unit; the area is in that unit squared. A warning is shown when the triangle is right-angled, as the Pythagorean theorem calculator then also applies.
Which calculators should I use next?
Common next steps are Pythagorean Theorem (Right Triangle) Calculator, Trigonometry (Sin, Cos, Tan), Circle Calculator (Radius, Diameter, Circumference, Area) and Phasor Sum and Difference (Polar Inputs). The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 35 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Trigonometry Formulas for Electrical Engineers: Sine, cosine and tangent formulas for engineers: the six trig functions, degrees and radians
- Power Factor and the Power Triangle: Power factor formulas: kW, kVA and kVAR from the power triangle, capacitor kVAR to raise power factor
- Complex Number Formulas: Polar and Rectangular: Complex number formulas for engineers: rectangular and polar form, conversion with atan2, addition
More Engineering Mathematics calculatorsAll engineering calculatorsTriangle Calculator (Three Sides) in Elecmetric