Triangle Calculator

Triangle Calculator

Solve all properties of a triangle including sides, angles, area, heights, and medians with step-by-step logic.

Input Geometry
CABside bside aside c

Solver Configuration

Provide exactly three values (including at least one side) to solve the triangle. The engine supports ASA, AAS, SAS, and SSS configurations.

Results
Acute Scalene Triangle

a

4.0000

b

2.0000

c

3.0000

Angles
∠A

104.478°

104°28'39" • 1.82348 rad

∠B

28.955°

28°57'18" • 0.50536 rad

∠C

46.567°

46°34'3" • 0.81276 rad

Area

2.90474

Perimeter

9.00

Heights & Medians

Height (ha)

1.45237

Height (hb)

2.90474

Height (hc)

1.93649

Median (ma)

1.58114

Median (mb)

3.39116

Median (mc)

2.78388

Solve Any Geometric Triangle Instantly with MyApexCalc

Whether you are completing high school trigonometry homework, drafting architectural blueprints, measuring land plots, or working on a DIY woodworking project, calculating the dimensions of a triangle can quickly get complicated. Depending on the information you have on hand, finding missing side lengths, interior angles, or total surface coverage requires applying entirely different mathematical theorems. Our free online Triangle Calculator is engineered to do the heavy lifting for you, functioning as a comprehensive geometric solver and right triangle calculator that processes complex math in real-time.

Deciphering Geometric Math: Key Formulas for Triangles

Our calculation engine dynamically adapts to the inputs you provide. Depending on your available measurements, the calculator leverages several core mathematical frameworks to solve your shape:

1. Finding Area with Base and Height

The most common formula for triangle area is used when you already know the perpendicular height (h) and the length of the base (b). The classic triangle area formula is:

Area = 1/2 × b × h

2. Finding Area of Any Triangle (Heron's Formula)

If you do not know the height but have the lengths of all three sides (a, b, and c), you can still find area of triangle formula structures by first calculating the semi-perimeter (s):

s = (a + b + c) / 2

Once you have the semi-perimeter, Heron's Formula calculates the precise area (A):

A = √[s(s - a)(s - b)(s - c)]

3. Solving Right Triangles (Pythagorean Theorem)

For triangles containing a perfect 90° right angle, the relationship between the two perpendicular legs (a and b) and the longest diagonal side (the hypotenuse, c) is solved using the classic Pythagorean theorem:

a² + b² = c² ⟹ c = √(a² + b²)

If you only know one side and an angle, our tool utilizes trigonometric sine (sin), cosine (cos), and tangent (tan) ratios to compute every remaining angle and edge length instantly.

Core Triangle Properties Explained

Our interactive dashboard automatically categorizes your shape based on the dimensions you input:

  • Equilateral

    All three sides are of equal length, and all three internal angles are exactly 60°.

  • Isosceles

    Two sides are of equal length, and the angles opposite those sides are equal.

  • Scalene

    All three sides and all three interior angles have entirely different measurements.

  • Right Angle

    Contains one interior angle that measures exactly 90°.

Why Solve Geometric Shapes with MyApexCalc?

  • Multiple Input Modes: Choose from Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or simple Base-and-Height inputs.
  • Dynamic Visual Layout: Watch our interface automatically categorize your triangle and render a responsive structural preview.
  • Simultaneous Unit Conversions: Switch between millimeters, centimeters, inches, feet, and meters without losing your geometric values.

"Geometry is the foundation of design and construction. Solve your spatial problems with absolute mathematical certainty."