Geometry Calculator: Master Shapes, Areas & Volumes
Calculate area, perimeter, volume, and surface area for various geometric shapes. Supports both 2D and 3D shapes with metric and imperial measurements.
Shape Type
Select Shape
Measurement System
Dimensions
Shape Preview
Results
Area
0.00 cm²
Area = side × side
Perimeter
0.00 cm
Perimeter = 4 × side
Note: All calculations are approximate. For precise measurements, consult with a professional.
What It Does
Calculate area, perimeter, volume, and surface area for common 2D shapes (square, rectangle, triangle, circle) and 3D shapes (cube, sphere, cylinder, cone). Works with both metric (cm, m) and imperial (in, ft) units.
Useful for construction (material estimates, floor areas), DIY projects (paint coverage, room planning), homework, or any time you need to figure out dimensions and measurements.
FAQ
How do I calculate the area of a triangle?
Area = ½ × base × height. So if base is 10 and height is 6, area = ½ × 10 × 6 = 30 square units. For irregular triangles where you know all three sides, use Heron's formula.
What's the difference between area and perimeter?
Area is the space inside (square units like cm² or ft²). Perimeter is the distance around the outside (linear units like cm or ft). A 5×5 square has area 25 and perimeter 20.
How do I convert between metric and imperial?
1 inch = 2.54 cm, 1 foot = 30.48 cm, 1 meter = 3.28 feet. For area: 1 ft² = 929 cm², 1 m² = 10.76 ft². For volume: 1 ft³ = 28,317 cm³, 1 m³ = 35.31 ft³.
What's the formula for cylinder volume?
V = π × r² × h (radius squared times height times pi). So radius 3, height 10 = π × 9 × 10 = 90π ≈ 282.74 cubic units.
How do I find the surface area of a sphere?
SA = 4πr². Radius 5 = 4π × 25 = 100π ≈ 314.16 square units.
What value of π should I use?
3.14159 is fine for most things. The calculator uses high-precision π automatically.
How do I calculate a rectangle's diagonal?
Pythagorean theorem: diagonal = √(length² + width²). Length 8, width 6 = √(64 + 36) = √100 = 10 units.
What's the difference between circumference and diameter?
Diameter is straight across through the center. Circumference is the distance around the edge. C = π × diameter, or C = 2πr.
How do I calculate irregular shape areas?
Break them into simpler shapes (triangles, rectangles, circles), calculate each separately, then add/subtract as needed.
What's the formula for a circle sector area?
A = (θ/360°) × πr² if θ is in degrees, or A = ½θr² if θ is in radians. It's just the fraction of the full circle's area.
How do I calculate cone volume?
V = ⅓πr²h (one-third of a cylinder with the same base and height). Radius 4, height 9 = ⅓π × 16 × 9 = 48π ≈ 150.8 cubic units.
What are common geometry mistakes?
Mixing up radius and diameter, using wrong units (mixing linear with square units), forgetting to square the radius in circle formulas, using degrees instead of radians or vice versa.