Surface Area Calculator
Calculate the surface area of 9 common 3D shapes instantly — formulas included.
Sphere Surface Area
SA = 4πr²Sphere
Please enter a valid radius greater than 0.
Surface Area
Cube Surface Area
SA = 6a²Cube
Please enter a valid edge length greater than 0.
Surface Area
Cylinder Surface Area
SA = 2πr(r + h)Cylinder
Please enter valid values greater than 0.
Total Surface Area
Cone Surface Area
SA = πr(r + √(r² + h²))Cone
Please enter valid values greater than 0.
Total Surface Area
Rectangular Box Surface Area
SA = 2(lw + lh + wh)Rectangular Box
Please enter valid values greater than 0.
Surface Area
Capsule Surface Area
SA = 4πr² + 2πrhCapsule
Please enter valid values greater than 0.
Surface Area
Square Pyramid Surface Area
SA = a² + 2a√((a/2)² + h²)Square Pyramid
Please enter valid values greater than 0.
Total Surface Area
Conical Frustum Surface Area
SA = π(R² + r²) + π(R+r)√((R−r)² + h²)Conical Frustum
Please enter valid values greater than 0.
Total Surface Area
Ellipsoid Surface Area
SA ≈ 4π((a¹·⁶b¹·⁶ + a¹·⁶c¹·⁶ + b¹·⁶c¹·⁶)/3)^(1/1.6)Ellipsoid
Uses Knud Thomsen's approximation formula.
Please enter valid values greater than 0.
Surface Area (approx.)
Surface Area Formulas Reference
| Shape | Formula | Variables |
|---|---|---|
| Sphere | SA = 4πr² | r = radius |
| Cube | SA = 6a² | a = edge length |
| Cylinder | SA = 2πr(r + h) | r = radius, h = height |
| Cone | SA = πr(r + √(r²+h²)) | r = base radius, h = height |
| Rect. Box | SA = 2(lw + lh + wh) | l = length, w = width, h = height |
| Capsule | SA = 4πr² + 2πrh | r = radius, h = cylinder height |
| Sq. Pyramid | SA = a² + 2a√((a/2)²+h²) | a = base edge, h = height |
| Con. Frustum | SA = π(R²+r²) + π(R+r)√((R−r)²+h²) | R = bottom radius, r = top radius, h = height |
| Ellipsoid | SA ≈ 4π·((a^p·b^p + a^p·c^p + b^p·c^p)/3)^(1/p), p≈1.6 | a, b, c = semi-axes |
What Is Surface Area?
Surface area is the total area of all the outer faces of a three-dimensional object. It is measured in square units (cm², m², in², ft², etc.). Engineers, architects, students, and scientists use surface area calculations for material estimation, heat transfer, painting, packaging, and more.
How to Use This Calculator
Select a shape from the tabs above, enter the required measurements in your preferred unit, and click Calculate. The result appears instantly along with a step-by-step formula breakdown. Click Clear to reset and start a new calculation.
Supported 3D Shapes
Sphere
SA = 4πr²Cube
SA = 6a²Cylinder
SA = 2πr(r+h)Cone
SA = πr(r+√(r²+h²))Rectangular Box
SA = 2(lw+lh+wh)Capsule
SA = 4πr²+2πrhSquare Pyramid
SA = a²+2a√((a/2)²+h²)Conical Frustum
SA = π(R²+r²)+π(R+r)√(…)Ellipsoid
Knud Thomsen approx.Common Area Unit Conversions
| Unit | Equals (in m²) |
|---|---|
| 1 km² | 1,000,000 m² |
| 1 cm² | 0.0001 m² |
| 1 mm² | 0.000001 m² |
| 1 ft² | 0.092903 m² |
| 1 in² | 0.00064516 m² |
| 1 yd² | 0.836127 m² |
Frequently Asked Questions
What is the surface area of a sphere with radius 5 cm?+
Using SA = 4πr², substitute r = 5: SA = 4 × π × 25 = 314.159 cm².
What is the difference between surface area and volume?+
Surface area measures the total outer face area of a 3D object (in square units), while volume measures the amount of space it occupies (in cubic units). For example, a box can have a large surface area but a small volume if it is very flat.
Why is the ellipsoid formula approximate?+
Unlike simpler shapes, there is no closed-form exact formula for an ellipsoid's surface area. This calculator uses Knud Thomsen's approximation, which is accurate to within about 1.061% for most practical ellipsoids.
How do I find the lateral surface area of a cylinder?+
The lateral (side only) surface area of a cylinder is 2πrh. The total surface area (including both circular caps) is 2πr(r + h). This calculator returns the total surface area.
What units does this calculator use?+
You can enter values in meters, centimeters, millimeters, kilometers, inches, feet, or yards using the unit selector. The result is shown in the squared version of the selected unit (e.g., if you choose "ft", the result is in ft²).