Oblique Triangle Calculator

Calculate angles, area, perimeter, radii, altitudes, and medians based on three provided side lengths. Oblique Triangle Calculator helps students, engineers, surveyors, and professionals analyze triangle geometry accurately.

Highlights

  • Calculate all three angles from the lengths of the triangle’s sides.
  • Find the triangle’s area, perimeter, and semiperimeter.
  • Determine altitudes and medians to each side.
  • Calculate the circumradius and inradius.
  • Supports multiple length and angle units for flexible calculations.

Table of Contents

  1. How Oblique Triangle Calculator Works?
  2. Practical Use Cases
  3. Accuracy and Limitations
  4. Quick Examples
  5. Frequently Asked Questions (FAQs)
  6. Cite This Calculator

How Oblique Triangle Calculator Works?

An oblique triangle has no right angle, so its geometry is determined from the three supplied side lengths a, b, and c. The calculator first checks the triangle inequality: the sum of any two sides must be greater than the third side. If this condition is satisfied, it calculates the angles, area, perimeter, semiperimeter, altitudes, medians, circumradius, and inradius.

The angles opposite the corresponding sides are found with the law of cosines:

A=cos−1b2+c2−a22bc
B=cos−1a2+c2−b22ac,C=cos−1a2+b2−c22ab

The perimeter and semiperimeter are calculated as follows:

P=a+b+c,s=P2

Heron's formula determines the enclosed area from the three sides:

K=s(s−a)(s−b)(s−c)

Using the same area, the perpendicular altitudes are:

ha=2Ka,hb=2Kb,hc=2Kc

The medians from the opposite vertices to the side midpoints use Apollonius's theorem:

ma=2b2+2c2−a22

The expressions for mb and mc follow by cycling the side labels. Finally, the circumradius and inradius are obtained from:

R=abc4K,r=Ks

ResultMathematical basis
Angles A, B, and CLaw of cosines
AreaHeron's formula
Perimeter and semiperimeterSide addition and half-perimeter
AltitudesTwo times area divided by the corresponding side
MediansApollonius's theorem
RadiiR = abc/(4K) and r = K/s

Side inputs support mm, cm, m, km, in, ft, yd, and mi. Length-based outputs use the corresponding supported length units, area uses the corresponding squared units, and angles can be displayed in degrees, radians, or grads.

Practical Use Cases

Students: Students can enter three known side lengths to verify homework involving the law of cosines, Heron's formula, medians, altitudes, and triangle radii. The detailed results help connect individual formulas with the complete geometry of an oblique triangle.

Engineers: Engineers can use the calculator during preliminary structural, mechanical, or layout analysis when three measured or designed sides define a triangular component. The angles, area, perimeter, and radii provide quick reference values before more detailed modeling.

Surveyors: Surveyors can analyze a triangular site or measured control shape from three side lengths. The calculated angles and altitudes support geometric checks, while area and perimeter provide useful planning quantities.

Construction and design professionals: Builders, fabricators, and design professionals can estimate triangular panel dimensions, material coverage, boundary length, and centerline-related geometry through the median results. Inputs may be entered in supported length units such as mm, cm, m, km, in, ft, yd, or mi.

Accuracy and Limitations

The calculator uses standard double-precision numerical formulas for the law of cosines, Heron's formula, altitude and median relationships, and the circumradius and inradius equations, so ordinary valid inputs are typically accurate to the displayed precision. All three side lengths must be positive and satisfy the strict triangle inequality; otherwise, no real triangle exists and area-based results cannot be calculated. Extremely large values up to the supported input limit of 1,000,000,000, very small sides near 0.01, or nearly degenerate triangles can magnify floating-point rounding, especially for angles close to 0 or 180 degrees and for Heron's formula when the area is very small. The results describe an ideal planar triangle and do not account for measurement error, curvature, thickness, or physical construction tolerances.

Quick Examples

Example #1: Classic 3-4-5 Triangle

Uses a standard right triangle to demonstrate basic oblique triangle calculations with familiar side lengths.

Example #2: Scalene Construction Triangle

Analyzes a non-isosceles triangle with unequal side lengths for construction and surveying applications.

Example #3: Small-Scale Engineering Triangle

Calculates detailed geometric properties for a compact triangle measured in centimeters.

Frequently Asked Questions

An oblique triangle is any triangle that does not contain a right angle. It may be acute, with all angles less than 90°, or obtuse, with one angle greater than 90°.

The sum of any two side lengths must be greater than the third side. If this condition is not met, the lengths cannot form a valid triangle.

An altitude is a perpendicular line from a vertex to the opposite side or its extension. A median connects a vertex to the midpoint of the opposite side.

The inradius is the radius of the circle inside the triangle that touches all three sides. The circumradius is the radius of the circle passing through all three vertices.

Students, engineers, surveyors, architects, and construction professionals use oblique triangle measurements for geometry problems, site planning, structural layouts, and land measurement.

Cite This Calculator