Surface Area Calculator

Math

Calculate total and lateral surface areas of 3D solids including spheres, cylinders, cones, rectangular prisms, cubes, capsules, hemispheres, and pyramids with area unit conversions.

Presets:

SPHERE Total Surface Area (m²)

314.159265 m² (100.00π m²) Volume: 523.5988 m³

Area Component Breakdown

Total Surface Area 314.1593 m²

Area Across Units (Converted from m²)

Square Meters (m²) 314.1593

Square Feet (ft²) 3,381.5821

Square Inches (in²) 486,947.8038

Square Yards (yd²) 375.7313

Acres 0.07763

Hectares 0.031416

Calculation Steps

1 1. Sphere Surface Area Formula

A = 4 · π · r² = 4 × π × 5² = 100.00π ≈ 314.159265

Area of 4 great circles of the sphere.

2 2. Enclosed Volume

V = ⁴⁄₃ · π · r³ = ⁴⁄₃ × π × 5³ ≈ 523.598776

Interior 3D volume enclosed by this spherical surface.

How This Calculator Works

The surface area of a solid object is a measure of the total area that the surface of the object occupies. For polyhedra, it is the sum of the areas of its faces.

📐 Standard 3D Surface Area Formulas

Sphere: A = 4πr² | Cylinder: A = 2πr(r + h) | Cone: A = πr(r + s) | Box: A = 2(lw + lh + wh)

Lateral Surface Area: The surface area of the 3D solid excluding its top and bottom base faces

Cone Slant Height (s): s = √(r² + h²)

Square Pyramid: A = b² + 2bs where slant s = √((b/2)² + h²)

Hemisphere: Closed solid: 3πr² (curved dome 2πr² + flat circular base πr²)

Key Mathematical Rules & Properties

Net Unfolding

Surface area can be verified by conceptually slicing and unfolding a 3D solid into a 2D net of planar figures.

Understanding your calculation

Method, example and limitations

How the calculation works

Surface area adds the exposed faces or curved surfaces of a solid. The chosen formula depends on the shape and whether it is open or closed.

Example to check

A closed cube with side length 2 has six faces of area 4, for total surface area 24 square units.

Before using the result

An open container excludes missing faces. Paint or material ordering may also require allowances for overlaps, openings and waste.

Calculation methodology · Report a result that needs review