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📐 Surface Area Calculators

Free online calculators for finding the surface area of any 3D shape. Accurate formulas, step-by-step solutions, and educational content.

What is Surface Area?

Surface area is the total area of all faces (surfaces) of a 3D object. It's measured in square units (cm², m², in²) and is essential for calculating materials needed for covering, painting, or wrapping objects.

Choose Your Calculator

Cone Surface Area

Calculate lateral and total surface area of cones using radius and slant height.

A = πr² + πrl

Truncated Cone (Frustum)

Surface area of a cone with the top cut off. Uses both radii and slant height.

A = π(R² + r² + (R+r)l)

Cube Calculator

Surface area, volume, and diagonals of a cube from any known value.

A = 6a²

Cylinder Calculator

Calculate surface area, volume, radius, or height of cylinders.

A = 2πr(r + h)

Pipe Calculator

Hollow cylinder calculations: inner/outer surfaces, volume, weight.

A = 2π(RL + rL + R² - r²)

Rectangular Pyramid

Surface area and volume of pyramids with rectangular bases.

A = lw + lateral faces

Rectangular Box (Prism)

Surface area, volume, and diagonals of rectangular prisms.

A = 2(lw + lh + wh)

Sphere Calculator

Calculate surface area, volume, and radius of spheres.

A = 4πr²

Torus Calculator

Donut-shaped surface area and volume from major and minor radii.

A = 4π²Rr

Triangular Prism

Surface area and volume of prisms with triangular bases.

A = 2×TriArea + P×L

Tube Surface Area

Inner, outer, and total surface area of hollow cylindrical tubes.

Atotal = inner + outer + ends

Quick Reference: Surface Area Formulas

Shape Surface Area Formula Key Variables
Cube A = 6a² a = side length
Rectangular Prism A = 2(lw + lh + wh) l, w, h = dimensions
Sphere A = 4πr² r = radius
Cylinder A = 2πr(r + h) r = radius, h = height
Cone A = πr(r + l) r = base radius, l = slant
Pyramid A = Base + Lateral Varies by base shape
Triangular Prism A = 2B + Ph B = base area, P = perimeter
Torus A = 4π²Rr R = major, r = minor radius

Understanding Surface Area

📏 What is Surface Area?

Total area of all outer faces of a 3D object. Think of it as the amount of wrapping paper needed to cover the entire shape.

📐 Area vs Surface Area

Area is 2D (flat shapes). Surface area is the sum of all 2D areas that make up a 3D shape's exterior.

🎨 Practical Uses

Painting, coating, packaging, heat transfer, material estimation. Essential for manufacturing, construction, and science.

📦 Lateral vs Total

Lateral: side surfaces only. Total: all surfaces including top/bottom. Different uses require different calculations.

Frequently Asked Questions

What is the difference between area and surface area?
Area applies to 2D shapes (circles, rectangles). Surface area is the total of all areas covering a 3D object. A box has 6 rectangular areas that sum to its surface area.
What is the surface area of a rectangular prism?
A = 2(lw + lh + wh). Add the areas of all 6 faces: 2 sides of l×w, 2 of l×h, and 2 of w×h. Also called a cuboid or rectangular box.
How do I find the surface area of a pyramid?
A = Base Area + Lateral Area. Base depends on shape (square, rectangle, triangle). Lateral area = sum of triangular faces. Need slant heights.
What is the surface area formula for a triangular prism?
A = 2B + Ph. B = triangular base area, P = triangle perimeter, h = prism length. Two triangular ends + three rectangular faces.
How do I calculate surface area of a triangular pyramid?
A = Base + 3 triangular faces. For regular tetrahedron: A = √3 × a². For other pyramids, calculate each face separately.
What is total surface area vs lateral surface area?
Lateral: sides only, excludes top and bottom. Total: all surfaces. For a cylinder: lateral = 2πrh, total = 2πr(r+h).
How do I find the surface area of a sphere?
A = 4πr². Four times pi times radius squared. The sphere has the minimum surface area for a given volume.
What is the surface area of a cube?
A = 6a². Six identical square faces, each with area a². All edges equal length a.
How do I find the surface area of a cylinder?
Total: A = 2πr(r + h). Lateral only: A = 2πrh. Two circular ends (πr² each) plus curved side (2πrh).
What is the surface area of a cone?
A = πr(r + l). Base (πr²) plus lateral (πrl). Need slant height l, not vertical height. l = √(r² + h²).
How do prism calculator surface area tools work?
They use standard geometric formulas. Input dimensions, calculator applies formula, shows step-by-step solution. Works for any valid measurements.
What units should I use for surface area?
Square units: cm², m², in², ft². Keep all input measurements in the same unit. Output will be in that unit squared.
How does doubling size affect surface area?
Surface area increases 4×. Since SA involves length², doubling all dimensions gives (2)² = 4 times the area. Volume increases 8×.
What is the surface area of a hollow cylinder (pipe/tube)?
A = outer + inner + ends. Outer: 2πRL, Inner: 2πrL, Ends: 2π(R²-r²). Total = 2π[RL + rL + R² - r²].
How do I calculate surface area for irregular shapes?
Break into simpler shapes. Calculate each part separately, then sum. May need to subtract overlapping areas.
What is the surface area of a torus (donut)?
A = 4π²Rr. R = major radius (center to tube), r = minor radius (tube radius). Product of two circumferences.
Why is surface area important?
Material estimation, heat transfer, chemical reactions, packaging. More surface area = more interaction with surroundings. Critical in engineering and science.