Pythagorean Theorem Calculator

Pythagorean Theorem is evaluated from Solve For, Side a and Side b. The calculation reports Missing Side, Triangle Area and Triangle Perimeter.

Results

Thanks — we’ve logged this for review.

About the Pythagorean Theorem Calculator

Pythagorean Theorem is treated here as a quantitative relation between Solve For, Side a, Side b and Side c and Missing Side, Triangle Area, Triangle Perimeter and Is a Right Triangle?.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
c = sqrt(a^2 + b^2)
a = sqrt(c^2 - b^2)
b = sqrt(c^2 - a^2)

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

c = sqrt(a^2 + b^2)
a = sqrt(c^2 - b^2)
b = sqrt(c^2 - a^2)

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Staircase Ramp Length

Inputs

solve_for: c a_val: 9 b_val: 40
Missing Side: 41. Triangle Area: 180 sq units. Triangle Perimeter: 90 units. Is a Right Triangle?: Yes - Right Triangle

With Solve For = c, Side a = 9 and Side b = 40 as the stated inputs, the result is Missing Side = 41, Triangle Area = 180 sq units and Triangle Perimeter = 90 units. Each value corresponds to the declared output fields.

Example 2: Room Diagonal — TV Viewing Distance

Inputs

solve_for: c a_val: 15 b_val: 20
Missing Side: 25. Triangle Area: 150 sq units. Triangle Perimeter: 60 units. Is a Right Triangle?: Yes - Right Triangle

With Solve For = c, Side a = 15 and Side b = 20 as the stated inputs, the result is Missing Side = 25, Triangle Area = 150 sq units and Triangle Perimeter = 60 units. Each value corresponds to the declared output fields.

Example 3: Diagonal Fence Post — Squaring a Layout

Inputs

solve_for: c a_val: 6 b_val: 8
Missing Side: 10. Triangle Area: 24 sq units. Triangle Perimeter: 24 units. Is a Right Triangle?: Yes - Right Triangle

With Solve For = c, Side a = 6 and Side b = 8 as the stated inputs, the result is Missing Side = 10, Triangle Area = 24 sq units and Triangle Perimeter = 24 units. Each value corresponds to the declared output fields.

Example 4: Check if Triangle is Right

Inputs

solve_for: check a_val: 5 b_val: 12 c_val: 13
Missing Side: 13. Triangle Area: 30 sq units. Triangle Perimeter: 30 units. Is a Right Triangle?: Yes - Right Triangle

With Solve For = check, Side a = 5, Side b = 12 and Side c = 13 as the stated inputs, the result is Missing Side = 13, Triangle Area = 30 sq units and Triangle Perimeter = 30 units. Each value corresponds to the declared output fields.

Common Use Cases

  • Find hypotenuse of a right triangle
  • Calculate diagonal distance across a rectangular room
  • Determine ramp length for a given rise and run
  • Verify whether a triangle is a right triangle