Geometry Calculator (Right Triangle, Circle & Cylinder)

Solve right triangles, circles, and cylinders with live dimension-labeled SVG schematics.

Hypotenuse (c) & Triangle Area
c = 5 • Area = 6
Perimeter: 12 • Angles: α = 36.87°, β = 53.13°, γ = 90°
Hypotenuse (c = √(a²+b²)) 5
Area (½ab) 6
Perimeter (a+b+c) 12
Internal Angles (α, β) 36.9° & 53.1°
Inputs
Select 2D or 3D geometric figure.
units
Base leg a (for triangle) or radius r (for circle/cylinder).
units
Vertical leg b (for triangle) or height h (for cylinder).
Results & Graph
Hypotenuse (c) & Triangle Area
c = 5 • Area = 6
Perimeter: 12 • Angles: α = 36.87°, β = 53.13°, γ = 90°
Hypotenuse (c = √(a²+b²))
5
Area (½ab)
6
Perimeter (a+b+c)
12
Internal Angles (α, β)
36.9° & 53.1°

Dimension-Labeled Right Triangle Diagram

Interactive SVG diagram showing legs a, b, hypotenuse c, and acute angles
Graph 1 • Dimensioned Geometric Blueprint Schematic Labeled sides, radius, height, and interior angles
a = 3 b = 4 c = 5 α = 36.9° β = 53.1°
Graph 2 • Linear Dimensions & Pythagorean Hypotenuse / Diameter Direct comparison of side lengths and diagonal span
Primary Dimension (a or r) 6 units Secondary Dimension (b or h) 8 units Hypotenuse / Diameter √(a²+b²) 10.00 units
Graph 3 • How Doubling Dimensions Scales Area (4×) & Volume (8×) Quadratic (k²) surface scaling vs. cubic (k³) volume scaling
0 248.8 497.7 0.5× Dim: 12 12 0.5× Dim 0.75× Dim: 27 27 0.75× Dim 1× Dim: 48 48 1× Dim 1.25× Dim: 75 75 1.25× Dim 1.5× Dim: 108 108 1.5× Dim 2× Dim: 192 192 2× Dim
Summary: Right triangle with legs a=3, b=4, hypotenuse c=5, and area 6.
Summary: A right triangle with legs a = 3 and b = 4 has hypotenuse c = 5 by the Pythagorean theorem, area A = 6, perimeter P = 12, and acute angles α = 36.87° and β = 53.13°.
⚡ Send result to: Scientific →Concrete & Sq Ft →Unit Converter →
Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Pythagorean, Circular & Cylindrical Identities

Triangle:   c = a2 + b2,   A = ab2
Circle:   A = πr2,   C = 2πr   |   Cylinder:   V = πr2h,   SA = 2πrh + 2πr2
Triangle: c = √(a² + b²), A = ½ab, α = arctan(a/b); Circle: A = πr², C = 2πr; Cylinder: V = πr²h, SA = 2πrh + 2πr²
  • a, b, c: Perpendicular legs a, b and hypotenuse c of a right triangle
  • r, h: Radius r and height h

Rounding: Rounded to 4 decimal places.

Worked Example: Classic 3–4–5 Right Triangle (a = 3, b = 4)

Solve hypotenuse, area, perimeter, and acute angles for a right triangle with legs a = 3 and b = 4.

  1. Hypotenuse c = √(3² + 4²) = √25 = 5.
  2. Area = 0.5 × 3 × 4 = 6 square units; Perimeter = 3 + 4 + 5 = 12 units.
  3. Angle α = arctan(3/4) = 36.87°; Angle β = arctan(4/3) = 53.13°.
Result: c = 5, Area = 6, Perimeter = 12, α = 36.87°, β = 53.13°.

Frequently Asked Questions

How do I convert the geometric area if my inputs are in feet?

If inputs are in feet, area is in square feet (ft²) and volume is in cubic feet (ft³). Use the Unit Conversion or Concrete Calculator to convert ft³ to cubic yards.

Mathematics & Statistics · Plane & Solid Geometry

Geometry Calculator (Right Triangle, Circle & Cylinder): inputs, method, and how to read the result

Solve right triangles, circles, and cylinders with live dimension-labeled SVG schematics.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Geometric Shape: Select 2D or 3D geometric figure.
  • Primary Dimension (Leg a or Radius r): Base leg a (for triangle) or radius r (for circle/cylinder).
  • Second Dimension (Leg b or Height h): Vertical leg b (for triangle) or height h (for cylinder).

What the calculation includes

With the default values shown, Hypotenuse (c) & Triangle Area is c = 5 • Area = 6. The calculation follows Pythagorean, Circular & Cylindrical Identities; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Geometric Shape from Right Triangle (Legs a & b → Hypotenuse c, Area, Angles) to Circle (Radius r → Diameter, Circumference, Area) changes Hypotenuse (c) & Triangle Area (c = 5 • Area = 6) to Circle Area (A = πr²) (28.2743 sq units). This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • All linear dimensions use the same unit of length (e.g., cm, m, in, ft).
  • Triangle mode assumes a 90° right angle between legs a and b.

Scope: Global Check the assumptions and limitations against your situation before relying on the estimate.

More in Mathematics & Statistics: Scientific Calculator, Concrete & Square Footage Calculator, Unit Conversion Calculator.