Enter at least 3 values (sides or angles) in the input boxes around the triangle diagram.
Select your preferred angle unit (degrees or radians) from the dropdown menu.
Click Calculate to solve the triangle and view all measurements, area, perimeter, and more.
Frequently asked questions
What methods can this calculator use to solve triangles?
This calculator can solve triangles using SSS (three sides), SAS (two sides and included angle), ASA (two angles and one side), AAS (two angles and one side), and SSA (two sides and non-included angle) methods.
What is the difference between degrees and radians?
Degrees and radians are two ways to measure angles. A full circle is 360° or 2π radians. To convert: degrees = radians × (180/π), radians = degrees × (π/180).
Check the units, assumptions and rounding before using a result. Health and financial estimates are educational and do not replace individual professional advice.
Found an error? Send the tool name, inputs, expected result and actual result so we can investigate.
Solve any triangle using SSS, SAS, ASA, AAS, and SSA methods. Calculate sides, angles, area, perimeter, heights, medians, and more
Triangle Solver
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What is a Triangle?
A triangle is a three-sided polygon with three vertices and three angles. The sum of all interior angles in a triangle always equals 180° (or π radians). Triangles can be classified by their sides (equilateral, isosceles, scalene) or by their angles (acute, right, obtuse). Our triangle calculator can solve any triangle when you provide at least three measurements: three sides (SSS), two sides and the included angle (SAS), two angles and one side (ASA or AAS), or two sides and a non-included angle (SSA - ambiguous case).
Triangle Notation
In our triangle calculator, we use standard notation where sides and angles are related as follows:
Side a is opposite to angle A (α)
Side b is opposite to angle B (β)
Side c is opposite to angle C (γ)
The sum of angles A + B + C is always 180° (or π radians).
📏 Triangle Medians
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Every triangle has three medians, which intersect at a single point called the centroid.
The centroid divides each median in the ratio 2:1, with the longer segment near the vertex.
⭕ Inradius (Inscribed Circle)
The inradius (r) is the radius of the inscribed circle (incircle), which is the largest circle that will fit inside the triangle.
r = (Area ÷ s) (where s = ((a+b+c) ÷ 2))
r=sArea(where s=2a+b+c)
The center of the incircle is called the incenter, where the angle bisectors meet.
🔵 Circumradius (Circumscribed Circle)
The circumradius (R) is the radius of the circumscribed circle (circumcircle), which passes through all three vertices of the triangle.
R = (abc ÷ (4 × Area))
R=4×Areaabc
The center of the circumcircle is called the circumcenter, where the perpendicular bisectors of the sides meet.
💡 Interesting Triangle Facts
• The sum of the lengths of any two sides of a triangle must be greater than the length of the third side (Triangle Inequality).
• The sum of the internal angles of a triangle is always 180 degrees.
• The largest side is always opposite the largest angle, and the smallest side is opposite the smallest angle.
• An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
• The centroid (intersection of medians) is the center of gravity of the triangle.
• In a right triangle, the midpoint of the hypotenuse is the circumcenter.
Law of Sines
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles. This law is particularly useful for solving triangles when you know two angles and one side (ASA or AAS) or two sides and a non-included angle (SSA).
(a ÷ A) = (b ÷ B) = (c ÷ C)
sinAa=sinBb=sinCc
Law of Cosines
The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is useful for solving triangles when you know three sides (SSS) or two sides and the included angle (SAS). This law is a generalization of the Pythagorean theorem.
c^2 = a^2 + b^2 - 2ab C
c2=a2+b2−2abcosC
Triangle Area Formula (Heron's Formula)
Heron's formula allows you to calculate the area of a triangle when you know all three sides. First calculate the semiperimeter s = (a + b + c)/2, then use the formula below. This is one of the most elegant formulas in geometry.
Area = √(s(s-a)(s-b)(s-c)) where s = ((a+b+c) ÷ 2)
Area=s(s−a)(s−b)(s−c) where s=2a+b+c
Triangle Calculation Examples
Example 1: Equilateral Triangle
An equilateral triangle has all three sides equal to 5 meters. Find all angles and the area.
You can use our calculator by entering:
What are the angles and area of an equilateral triangle with sides of 5 meters?
The calculator returns:
All angles are 60° (π/3 radians), Area = 10.825 m²
Solution Steps:
Given: All sides a = b = c = 5 meters
In an equilateral triangle, all angles are equal
Each angle = 180° / 3 = 60° = π/3 radians
Using area formula: Area = (√3/4) × 5² = 10.825 m²
The formula used is:
Area = (√(3) ÷ 4)a^2 = (√(3) ÷ 4)(5)^2 ≈ 10.825
Area=43a2=43(5)2≈10.825
Example 2: SSS - Three Sides Known
A triangle has sides of 7 cm, 8 cm, and 9 cm. Find all angles and the area.
From a point 500 meters from the base of a mountain, the angle of elevation to the peak is 35°. If the observer is at ground level, how tall is the mountain?
You can use our calculator by entering:
Find the height when horizontal distance = 500 m and angle = 35°.
The calculator returns:
Height ≈ 350.1 meters
Solution Steps:
Given: horizontal distance = 500 m, angle of elevation = 35°
Using right triangle trigonometry: tan(35°) = height / 500
height = 500 × tan(35°) ≈ 500 × 0.7002
height ≈ 350.1 meters
The formula used is:
h = 500 × (35°) ≈ 500 × 0.7002 ≈ 350.1
h=500×tan(35°)≈500×0.7002≈350.1
Example 5: Roof Truss Design
A roof truss has a horizontal beam of 8 meters. The two sloping beams meet at a peak 3 meters above the center. Find the length of each sloping beam.
You can use our calculator by entering:
Find the sloping beam length with base = 4 m (half of 8) and height = 3 m.
The calculator returns:
Each sloping beam = 5 meters
Solution Steps:
Half the base = 8/2 = 4 meters
Height = 3 meters
Using Pythagorean theorem: s² = 4² + 3²
s² = 16 + 9 = 25
s = 5 meters
The formula used is:
s = √(4^2 + 3^2) = √(16 + 9) = √(25) = 5
s=42+32=16+9=25=5
Example 6: ASA - Two Angles and Included Side
In surveying, two angles of a triangular plot are 45° and 75°, and the side between them is 50 meters. Find the other two sides.
You can use our calculator by entering:
Given ∠A = 45°, ∠C = 75°, b = 50 m, find sides a and c.
The calculator returns:
a ≈ 36.60 m, c ≈ 50.00 m
Solution Steps:
Given: ∠A = 45°, ∠C = 75°, b = 50 m
Find ∠B = 180° - 45° - 75° = 60°
Using Law of Sines: a/sin(45°) = 50/sin(60°)
a = 50 × sin(45°) / sin(60°) ≈ 36.60 m
Similarly, c ≈ 50.00 m
The formula used is:
(a ÷ 45°) = (50 ÷ 60°) a = ((50 × 45°) ÷ 60°)
sin45°a=sin60°50⇒a=sin60°50×sin45°
Example 7: Right Triangle (Special Case)
A right triangle has one leg of 6 cm and a hypotenuse of 10 cm. Find the other leg and all angles.
You can use our calculator by entering:
Given: one leg = 6 cm, hypotenuse = 10 cm, one angle = 90°.