Surface Area Calculator
Visually calculate the surface area of common 3D geometric shapes. Enter the dimensions to get the result instantly.
Surface Area = 6 × Side²
How to Calculate Cube Surface Area
The surface area of a cube is the sum of the areas of its six identical square faces. Since the area of one face is Side × Side (or s²), the total surface area is six times that value.
Formula: SA = 6s²
SA = 2(lw + lh + wh)
How to Calculate Cuboid Surface Area
A cuboid has three pairs of identical rectangular faces. To find the total surface area, you calculate the area of each unique face (length×width, length×height, and width×height), sum them up, and multiply by two.
Formula: SA = 2(lw + lh + wh)
Surface Area = 4πr²
How to Calculate Sphere Surface Area
The surface area of a sphere is four times the area of a circle with the same radius. It's calculated using Pi (π) and the square of the radius.
Formula: SA = 4πr²
SA = 2πrh + 2πr²
How to Calculate Cylinder Surface Area
The surface area of a cylinder is the sum of the areas of its two circular bases (2πr²) and the area of its curved side. The side, if unrolled, is a rectangle with a height equal to the cylinder's height and a width equal to the circle's circumference (2πr).
Formula: SA = 2πrh (side) + 2πr² (bases)
SA = πr(r + √(h² + r²))
How to Calculate Cone Surface Area
The surface area of a cone is the sum of the area of its circular base (πr²) and its lateral (side) area (πrl), where 'l' is the slant height. The slant height is found using the Pythagorean theorem: l = √(h² + r²).
Formula: SA = πr² (base) + πrl (side)
SA = lw + l√( (w/2)² + h² ) + w√( (l/2)² + h² )
How to Calculate Pyramid Surface Area
For a rectangular pyramid, the surface area is the area of the rectangular base (lw) plus the area of the four triangular faces. This requires calculating the slant heights of the side faces using the Pythagorean theorem.
Formula: SA = Base Area + Lateral Area
SA = 4π²Rr
How to Calculate Torus Surface Area
A torus is a donut-shaped object. Its surface area is calculated using its major radius (R), the distance from the center of the hole to the center of the tube, and its minor radius (r), the radius of the tube itself.
Formula: SA = 4π²Rr
SA = bh + (s1+s2+s3)L
How to Calculate Triangular Prism Surface Area
The surface area is the sum of the areas of the two triangular bases and the three rectangular sides. The area of the two bases is base × height. The area of the sides is the perimeter of the triangle (s1+s2+base) multiplied by the prism's length (L).
Formula: SA = (base × height) + (side1 + side2 + base) × Length
Understanding Surface Area for Each Shape
Cube
A cube has 6 identical square faces. To find its surface area, you calculate the area of one square face (side × side, or s²) and multiply it by 6. It's the total area of paper needed to wrap a perfect box.
Formula: SA = 6s²
Cuboid (Rectangular Prism)
A cuboid is a box-shape with 6 rectangular faces. It has three pairs of identical faces (top/bottom, front/back, left/right). The surface area is the sum of the areas of all these faces.
Formula: SA = 2(lw + lh + wh)
Sphere
A sphere is a perfectly round 3D object. Its surface area is the total area of its outer surface. Interestingly, the surface area of a sphere is exactly four times the area of a circle with the same radius.
Formula: SA = 4πr²
Cylinder
A cylinder consists of two circular bases and a curved side. Its surface area is the sum of the areas of the two circles (2 × πr²) and the area of the side. If you unroll the side, it becomes a rectangle with a height equal to the cylinder's height and a width equal to the circle's circumference (2πr).
Formula: SA = 2πrh + 2πr²
Cone
A cone has a circular base and a curved surface that tapers to a point (apex). Its surface area is the sum of the area of its circular base (πr²) and its lateral (side) area (πrl), where 'l' is the slant height. The slant height is the distance from the apex to the edge of the base.
Formula: SA = πr(r + l)
Pyramid (Rectangular Base)
A pyramid's surface area is the area of its base plus the area of all its triangular side faces. For a rectangular pyramid, this is the base area (lw) plus the area of the two pairs of triangular faces. Calculating the area of the side faces requires finding their slant heights.
Formula: SA = Base Area + Lateral Area
Torus
A torus is a donut-shaped surface generated by revolving a circle in three-dimensional space about an axis. Its surface area depends on the major radius (R), from the center of the hole to the center of the tube, and the minor radius (r), the radius of the tube itself.
Formula: SA = 4π²Rr
Triangular Prism
A triangular prism has two identical triangular bases and three rectangular sides. Its total surface area is the sum of the areas of the two triangular bases and the areas of the three rectangular sides. The area of the rectangular sides is found by multiplying the prism's length by the perimeter of the triangular base.
Formula: SA = (Base × Height) + (s1+s2+s3) × Length
Frequently Asked Questions
What is surface area?
Surface area is the total area that the surface of a three-dimensional object occupies. It's like the "skin" of the object. It is measured in square units (e.g., m², ft²).
What is the difference between surface area and volume?
Surface area is a two-dimensional measurement of the outer surface of an object. Volume is a three-dimensional measurement of the space inside an object. For example, the surface area of a box is the amount of wrapping paper needed to cover it, while the volume is the amount of space inside it.
What is slant height?
Slant height (often denoted as 'l') is the distance from the apex (tip) of a cone or pyramid down its side to a point on the edge of its base. It is different from the perpendicular height ('h') and is crucial for calculating surface area.