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°.

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 Guide

How to Use the Geometry Calculator (Right Triangle, Circle & Cylinder): Practical Guide & Visual Analysis

Compute exact geometric properties, Pythagorean hypotenuse, acute angles α and β, circle area and circumference, and cylinder volume/surface area, paired with a live annotated SVG diagram. Whether you are researching right triangle calculator, pythagorean theorem calculator, circle area circumference, cylinder volume calculator, hypotenuse calculator, this interactive tool helps you calculate hypotenuse, area, perimeter, circumference, volume, and internal angles with an interactive, dimension-labeled SVG geometric diagram.

Interpreting the 3 Custom Visual Graphs & Key Outputs

As you adjust Geometric Shape, Primary Dimension (Leg a or Radius r), Second Dimension (Leg b or Height h), the calculator immediately computes Hypotenuse / Area / Volume, Perimeter / Circumference / Surface Area, Internal Angles α and β (Degrees), Annotated SVG Diagram and updates all three domain-specific SVG charts in real time. Instead of relying on a single static figure, you can inspect the primary domain diagram, component breakdown, and multi-point trajectory curve to see how changing your inputs shifts the final result. Use the Compare (up to 3 scenarios) button to evaluate side-by-side variations before making a decision.

Real-World Benchmark & Planning Tips (Global)

In our benchmark scenario (Classic 3–4–5 Right Triangle (a = 3, b = 4)), c = 5, Area = 6, Perimeter = 12, α = 36.87°, β = 53.13°. Keep in mind that all linear dimensions use the same unit of length (e.g., cm, m, in, ft). For related calculations in Mathematics & Statistics, explore Scientific Calculator, Concrete & Square Footage Calculator, Unit Conversion Calculator.