Surface Area Calculator

What is Surface Area?

Surface Area is the total area that the surface of a three-dimensional object occupies. It represents the sum of all exposed areas of an object, typically measured in square units. The SI unit for surface area is the square meter (m²).

Surface Area Formulas

Shape	Surface Area Formula
Sphere	$A = 4 π r^{2}$
Cone	$A = π r (r + \sqrt{h^{2} + r^{2}})$
Cube	$A = 6 a^{2}$
Cylinder	$A = 2 π r (r + h)$
Rectangular Prism	$A = 2 (l w + l h + w h)$
Capsule	$A = 4 π r^{2} + 2 π r (h - 2 r)$
Spherical Cap	$A = 2 π R h$
Conical Frustum	$A = π (r + R) \sqrt{h^{2} + (R - r)^{2}} + π r^{2} + π R^{2}$
Ellipsoid	$A \approx 4 π {(\frac{a^{p} b^{p} + a^{p} c^{p} + b^{p} c^{p}}{3})}^{\frac{1}{p}}$ (p ≈ 1.6075)
Square Pyramid	$A = a^{2} + 2 a \sqrt{\frac{a^{2}}{4} + h^{2}}$

Unit Conversions

Unit	Conversion to Feet
1 mile	5280 feet
1 yard	3 feet
1 inch	1/12 feet
1 kilometer	3280.84 feet
1 meter	3.28084 feet
1 centimeter	0.0328084 feet

Surface Area Unit Conversions

Unit	Conversion from Square Feet
1 square foot	0.092903 square meters
1 square foot	929.03 square centimeters
1 square foot	144 square inches
1 square foot	0.000022957 acres

Frequently Asked Questions (FAQs) About Surface Area Calculation

What is the formula for calculating the surface area of a rectangular prism?

The surface area of a rectangular prism is calculated using the formula: Surface Area = 2 (Length × Width + Length × Height + Width × Height).

How do I calculate the surface area of a cylinder?

The surface area of a cylinder is calculated using the formula: Surface Area = 2π × Radius (Radius + Height).

Can I use a surface area calculator for irregular shapes?

Yes, advanced calculators can approximate the surface area of irregular shapes using numerical methods or 3D modeling software.

What units should I use for surface area calculation?

Common units include square meters (m²), square centimeters (cm²), and square feet (ft²). Consistency in units is key for accuracy.

How do I calculate the surface area of a sphere?

The surface area of a sphere is calculated using the formula: Surface Area = 4π × Radius².

What is the surface area of a cone, and how is it calculated?

The surface area of a cone is calculated using the formula: Surface Area = π × Radius (Radius + √(Height² + Radius²)).

Can I calculate the surface area of a pyramid?

Yes, for a square pyramid, use: Surface Area = Base Area + 2 × Base Side × √((Base Side² / 4) + Height²).

How do I convert surface area units, such as square meters to square feet?

To convert square meters to square feet, multiply by 10.7639 (1 m² ≈ 10.7639 ft²).

What is the importance of surface area calculation in real life?

Surface area calculations are vital in construction, packaging, painting, and heat transfer analysis for determining material needs and costs.

Are there online tools for surface area calculation?

Yes, numerous free online tools allow you to calculate surface area by entering dimensions for various shapes.

What is a Surface Area Calculator?

Surface Area For All Shapes

What is Surface Area?

Surface Area Formulas

Unit Conversions

Surface Area Unit Conversions

Frequently Asked Questions (FAQs) About Surface Area Calculation