⭕ Sphere Calc: find V, A, d
Calculate volume, surface area, and diameter of a sphere
How to Use This Calculator
Select What You Know
Choose from the dropdown: Radius (r), Diameter (d), Volume (V), or Surface Area (A). Select the value you already have.
Enter the Value
Input the known value in the input field. Make sure it's a positive number in consistent units.
Get All Results
Click "Calculate" to instantly get the radius, diameter, volume, and surface area. All values are calculated from your input.
Formulas
Volume: V = (4/3)πr³
Four-thirds times pi times radius cubed
Surface Area: A = 4πr²
Four times pi times radius squared
Diameter: d = 2r
Twice the radius
Where:
- r = radius of the sphere
- d = diameter of the sphere
- V = volume
- A = surface area
- π ≈ 3.14159
Example 1: From Radius
Given: r = 5 units
d = 2 × 5 = 10 units
V = (4/3) × π × 5³ = (4/3) × π × 125 = 500π/3 ≈ 523.60 units³
A = 4 × π × 5² = 4 × π × 25 = 100π ≈ 314.16 units²
Example 2: From Volume
Given: V = 288π units³
r = ∛(3 × 288π/(4π)) = ∛(216) = 6 units
d = 2 × 6 = 12 units
A = 4 × π × 6² = 144π ≈ 452.39 units²
Example 3: From Surface Area
Given: A = 64π units²
r = √(64π/(4π)) = √16 = 4 units
d = 2 × 4 = 8 units
V = (4/3) × π × 4³ = 256π/3 ≈ 268.08 units³
About Sphere Calculator: Find V, A, d
A sphere is a perfectly round 3D shape where all points on the surface are equidistant from the center. This calculator allows you to find any sphere property (volume V, surface area A, diameter d, or radius r) from just one known value. The sphere is one of the most symmetrical shapes in geometry.
When to Use This Calculator
- Geometry Problems: Solve sphere-related problems when you know one dimension
- Physics: Calculate sphere properties for physics problems (density, volume, surface area)
- Engineering: Determine material requirements when only one sphere property is known
- Packaging: Find sphere dimensions for spherical containers or balls
- Mathematics Education: Teach students relationships between sphere properties
- 3D Design: Work with sphere models in CAD or design software
Why Use Our Calculator?
- ✅ Flexible Input: Start with radius, diameter, volume, or surface area - we calculate the rest
- ✅ Complete Results: Get all sphere properties (V, A, d, r) at once
- ✅ Step-by-Step Display: See the formulas and calculations used
- ✅ 100% Accurate: Uses precise mathematical relationships
- ✅ Instant Calculations: No manual formula solving required
- ✅ Completely Free: No registration required
Understanding Sphere Relationships
All sphere properties are mathematically related:
- Volume (V): The amount of space inside = (4/3)πr³
- Surface Area (A): Total area covering the sphere = 4πr²
- Radius (r): Distance from center to surface
- Diameter (d): Distance through the center = 2r
- Relationship: All properties can be calculated from any one property
Real-World Applications
Sports: A basketball has a diameter of 24 cm. Radius = 12 cm, Volume ≈ 7,238.23 cm³, Surface Area ≈ 1,809.56 cm². This helps determine material needed and capacity.
Planetary Science: Earth has a radius of approximately 6,371 km. Volume ≈ 1.083 × 10¹² km³, Surface Area ≈ 510.1 million km². Essential for understanding Earth's size.
Engineering: A spherical tank has volume 100 m³. From volume, radius ≈ 2.88 m, diameter ≈ 5.76 m, and surface area ≈ 104.24 m² (for coating or material calculation).
Frequently Asked Questions
How do I find the radius from volume?
Rearrange the volume formula: V = (4/3)πr³, so r³ = 3V/(4π), and r = ∛(3V/(4π)). Take the cube root of (3V/(4π)). For example, if V = 288π, then r = ∛(3×288π/(4π)) = ∛216 = 6.
How do I find the radius from surface area?
Rearrange the surface area formula: A = 4πr², so r² = A/(4π), and r = √(A/(4π)). Take the square root of (A/(4π)). For example, if A = 64π, then r = √(64π/(4π)) = √16 = 4.
What's the relationship between volume and surface area?
For a sphere: V = (4/3)πr³ and A = 4πr². From volume: r = ∛(3V/(4π)), so A = 4π(∛(3V/(4π)))². The relationship is: A = (36π)¹/³ × V²/³, showing surface area is proportional to volume raised to the 2/3 power.
Can I calculate if I only know the diameter?
Yes! Diameter (d) = 2 × radius (r), so r = d/2. Once you have the radius, you can calculate volume and surface area. The calculator handles this automatically when you select "Diameter" as input.
Why is sphere volume (4/3)πr³?
This formula comes from calculus (integration) or geometric methods. The factor 4/3 appears because a sphere's volume is 4/3 times the volume of a cylinder that fits around it. The formula can be derived using integration of circular cross-sections.
What's the difference between a sphere and a circle?
A circle is 2D (has area), while a sphere is 3D (has volume and surface area). A circle's area is πr², while a sphere's surface area is 4πr² (four times larger). A sphere is the 3D equivalent of a circle.