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Kordu Tools
Math & Numbers Runs in browser Updated 30 Mar 2026

Triangle Calculator

Solve any triangle using SSS, SAS, ASA, AAS, or right-triangle mode. Get sides, angles, area, perimeter, and a live SVG diagram with step-by-step solutions.

Enter all values above to solve the triangle.

Key Formulae

Law of Cosines c² = a² + b² − 2ab·cos(C)

Law of Sines a/sin(A) = b/sin(B) = c/sin(C)

Heron's Formula Area = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2

SAS Area Area = 0.5 × a × b × sin(C)
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How to use Triangle Calculator

  1. Choose a solving mode

    Select SSS (three sides), SAS (two sides + angle), ASA (two angles + side), AAS (two angles + side), or Right Triangle from the tabs.

  2. Enter the known values

    Fill in the sides and angles you know. Leave unknown fields empty — the tool calculates them.

  3. View all triangle properties

    All missing sides, angles, area, and perimeter appear with labels identifying each result.

  4. Check the live SVG diagram

    The triangle diagram updates in real time as you enter values, giving a visual check on the geometry.

  5. Expand the step-by-step solution

    Click 'Show steps' to see which law (sines, cosines, or Pythagorean theorem) was applied and how.

Triangle Calculator FAQ

What do SSS, SAS, ASA, and AAS mean?
SSS = three sides known. SAS = two sides and the angle between them. ASA = two angles and the side between them. AAS = two angles and a non-included side.

What is the Pythagorean theorem?
For a right triangle: a² + b² = c², where c is the hypotenuse (side opposite the right angle). Enter any two sides in right-triangle mode to find the third.

What is the law of sines?
a/sin(A) = b/sin(B) = c/sin(C). Used when you know two angles and one side (ASA or AAS), or two sides and a non-included angle.

What is the law of cosines?
c² = a² + b² − 2ab·cos(C). Used when you know three sides (SSS) or two sides and the included angle (SAS).

How is triangle area calculated?
SAS mode uses Area = ½ × a × b × sin(C). SSS mode uses Heron's formula: s = (a+b+c)/2, Area = √(s(s−a)(s−b)(s−c)).

What if the triangle is impossible?
The calculator checks the triangle inequality theorem (sum of any two sides must exceed the third) and flags invalid inputs with a clear error.

How are triangle types detected?
Equilateral: all sides equal. Isosceles: two sides equal. Scalene: all different. Right: one 90° angle. Acute: all angles < 90°. Obtuse: one angle > 90°.

Can I solve an obtuse triangle?
Yes. All solving modes work for acute, right, and obtuse triangles. The law of cosines handles obtuse cases correctly.

Can I use this for homework?
Yes. The step-by-step solution shows which theorem was used and how values were substituted, making it ideal for checking your work.

Is any data sent to a server?
No. All calculations run entirely in your browser. Nothing is uploaded or stored.

Background

Enter any combination of known sides and angles to solve a triangle completely. Choose from five input modes: SSS uses the law of cosines to find all angles; SAS applies the law of cosines then law of sines; ASA and AAS use the law of sines; right-triangle mode applies the Pythagorean theorem and basic trigonometry. All missing sides, angles, area, and perimeter are calculated and displayed. The tool automatically detects triangle type: equilateral, isosceles, scalene, right, acute, or obtuse. A live SVG diagram updates as you change values, making it easy to visualize the triangle. Step-by-step solution is shown for each mode. The triangle inequality theorem is checked — invalid inputs trigger a clear error message. Useful for geometry, trigonometry, physics, surveying, and engineering. All processing runs in your browser.

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