Tools in This Collection
Pythagorean Theorem Calculator
Find the missing side of a right triangle using a² + b² = c²
Triangle Area Calculator
Calculate triangle area from base/height or any three sides using Heron's formula
Circle Calculator
Calculate area, circumference, arc length, and sector area from radius or diameter
Cylinder Volume Calculator
Calculate cylinder volume and surface area from radius and height
Sphere Calculator
Calculate sphere volume and surface area from radius or diameter
Geometry Calculation Workflow
Geometry calculations appear across construction, engineering, cooking, and everyday problem-solving. These tools cover the most common shape calculations with real-world examples and step-by-step working.
The Pythagorean Theorem Calculator finds the missing side of a right triangle given the other two sides: a² + b² = c². A 6-foot ladder leaning against a wall with its base 2 feet out touches the wall at √(36 - 4) = √32 = 5.66 feet. The same theorem determines if a corner is square in construction: a 3-4-5 right triangle (9 + 16 = 25) gives a perfect 90° angle. The calculator also works in reverse — give the hypotenuse and one leg to find the other.
Circle calculations are built on π (≈ 3.14159). A 10-inch diameter pizza has area = π × 5² = 78.5 square inches. A 14-inch diameter pizza has area = π × 7² = 153.9 square inches — 96% more pizza for about 30% more cost. Circumference = 2πr, so a circle with radius 8 has circumference 50.3 inches. The Circle Calculator computes area, circumference, arc length, and sector area from any input.
For 3D volumes, the Cylinder Volume Calculator uses V = πr²h. A cylindrical water tank 4 feet in diameter and 6 feet tall holds π × 2² × 6 = 75.4 cubic feet = 564 gallons. The Sphere Calculator uses V = (4/3)πr³. A sphere with 3-inch radius has volume (4/3) × π × 27 = 113 cubic inches. The Triangle Area Calculator handles all triangle types — right triangles, equilateral, isosceles — from any combination of sides and angles using Heron's formula when all three sides are known.
Frequently Asked Questions
How do I use the Pythagorean theorem in real life?
The Pythagorean theorem (a² + b² = c²) is useful whenever you have a right angle. In construction: check if a corner is square using a 3-4-5 triangle (3² + 4² = 5²). For ladders: a 10-foot ladder with its base 4 feet from a wall reaches √(100 - 16) = √84 = 9.17 feet up. For diagonal distances: a rectangle 12 feet wide and 9 feet long has a diagonal of √(144 + 81) = √225 = 15 feet.
What is the formula for the area of a circle?
Area = π × r² where r is the radius (half the diameter). For a 12-inch diameter circle, r = 6, so area = π × 36 = 113.1 square inches. For a 10-foot diameter circular garden, r = 5, area = π × 25 = 78.5 square feet. Circumference = 2 × π × r = π × diameter. The Circle Calculator accepts radius, diameter, area, or circumference and calculates all other values.
How do I calculate the volume of a cylinder?
Volume = π × r² × h where r is the radius and h is the height. For a cylinder 8 inches in diameter and 12 inches tall: r = 4, so volume = π × 16 × 12 = 603 cubic inches. To convert to gallons: 603 / 231 = 2.6 gallons. For a 4-foot diameter, 6-foot tall water tank: volume = π × 4 × 6 = 75.4 cubic feet = 564 gallons.