Can I rotate the 3D shape?

Yes — click and drag to rotate, scroll wheel (or pinch on touch) to zoom in and out. The viewer is built on OrbitControls from drei (a React Three Fiber helper). The shape automatically rescales to fill the viewport regardless of whether you entered millimeter values or kilometer values, so the visual is always proportional and readable.

Why isn't there a triangular prism?

This calculator focuses on the five most common solids — anything beyond that and the UI gets cluttered. For a triangular prism, the formula is simply V = base_area × height, so use the Triangle Solver to compute the base area first, then multiply by the prism's length. Same approach works for any prism with a polygonal base.

Does the calculator use π = 3.14 or full precision?

Full precision — JavaScript's Math.PI is approximately 3.141592653589793, which is accurate to about 15 decimal places (IEEE 754 double-precision floats). Way more accuracy than any physical measurement could ever justify. If your input dimensions are accurate to 3 decimals, your output is too — the pi precision isn't the limiting factor anywhere.

Premium Converters

3D Solid Volume Calculator

Math

Volume + surface area for sphere, cylinder, cone, cube, and rectangular prism. Interactive 3D visualization — rotate and zoom.

Math

3D Solid Volume Calculator

Generated on May 23, 2026

Shape

Radius (r)

Save / share— download or share to WhatsApp, Facebook & more

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Sphere Volume & Surface Area

V = 523.5988 units³ · A = 314.1593 units²

Generated

5/23/2026

Results

Volume

523.5988

cubic units (units³)

Surface area

314.1593

square units (units²)

Formula

V = ⁴⁄₃ π r³, A = 4 π r²

Loading 3D viewer…

💡 Click and drag the 3D shape to rotate it. Scroll to zoom.

Step-by-step calculation

Formula

V = ⁴⁄₃ π r³, A = 4 π r²

1Shape: Sphere
2r = 5. V = (4/3)π·5³ = 523.5988 units³.
3Surface area = 314.1593 square units.
4Units are unspecified — if your inputs are in cm the volume is in cm³, if in m then m³, etc.

Quick Answer

Volume + surface area for sphere, cylinder, cone, cube, and rectangular prism. Interactive 3D visualization — rotate and zoom.

Overview — 3D Solid Volume Calculator

Math

Formula

Sphere: V = ⁴⁄₃πr³, A = 4πr². Cylinder: V = πr²h, A = 2πr(r+h). Cone: V = ⅓πr²h, A = πr(r+√(r²+h²)). Cube: V = s³, A = 6s². Rectangular prism: V = lwh, A = 2(lw+lh+wh).

By Muhammad Salman SaleemUpdated: May 23, 2026MethodologyFree, no sign-upRuns in your browser — your data stays private

From the editors — what to know before you start

A civil engineer pricing a concrete pour for a 10 by 5 meter foundation at 0.3 m depth needs 15 cubic meters of mix. A homeowner installing a cylindrical water tank with radius 1 m and height 2 m gets 6,283 liters of capacity — almost exactly 6,283 because π × 1² × 2 × 1000 is a clean coincidence. A factory worker computing how much insulation foam fills a spherical pressure vessel uses (4/3)πr³. These five solids — sphere, cylinder, cone, cube, and rectangular prism — show up everywhere in real construction, packaging, and physics work, and getting their volume and surface area right matters when you're ordering 15 cubic meters of concrete that costs Rs 8,000 per cubic meter. The interactive 3D viewer (powered by Three.js) lets you rotate and zoom the shape, which is way more useful than it sounds — it catches input errors visually before they become spending errors. A tank that comes out impossibly tall on screen probably had radius and height swapped. Worth knowing one beautiful fact: the sphere has the smallest surface area for any given volume, which is exactly why bubbles, raindrops, and planets all converge on spherical shapes — surface tension and gravity both minimize surface area, and the sphere is the unique winner. A cube and a sphere of the same diameter have the cube holding nearly twice the volume of the sphere (the sphere takes only about 52 percent of the cube's volume).

Pro tips most people learn the hard way

Unit consistency is the silent killer. Putting radius in cm and height in m gives you a volume that looks like a real number but is total nonsense. Always stay within one unit system across a single calculation. The most common 'why does my answer look wrong' question on volume problems is always this.
A cone holds exactly one-third the volume of a cylinder with the same radius and height. So if you're scaling a recipe from a cylindrical tank to a conical hopper, multiply by 3 (cone to cylinder) or divide by 3 (cylinder to cone). This 1/3 relationship is true for any pyramid relative to its containing prism — beautiful piece of geometry.
Spheres minimize surface area for a given volume — that's why bubbles, raindrops, and ball bearings naturally form spheres. Conversely, cubes maximize volume for a given surface area among rectangular shapes (it's why suburban warehouses tend toward cubic proportions — most stored volume per dollar of wall and roof).
For real construction calculations, always pad your volume estimate by 5-10 percent for waste, spillage, and edge effects. A concrete pour that calculates to 15 cubic meters should be ordered as 16 to be safe. Running out mid-pour is much worse than having a little extra; the math is mathematically exact but the world is messy.
Surface area matters for cost almost as much as volume. Painting a cylinder, cladding a building, plating a sphere — all charge per unit area. A sphere of diameter 2 m has 12.57 m² of surface; a cube of side 2 m has 24 m². If the contents matter, calculate volume; if the wrapping matters, calculate surface area.

?What is the 3D Solid Volume Calculator?

The 3D Solid Volume Calculator computes both volume and surface area for the five most common solids — sphere, cylinder, cone, cube, and rectangular prism — and renders an interactive 3D model you can rotate and zoom. Powered by Three.js / React Three Fiber for true GPU-accelerated 3D (not just an isometric drawing). Useful for geometry homework, packaging design, civil engineering (concrete pours, water tank capacity), and any practical task that needs accurate solid measurements.

The Formula

Sphere: V = ⁴⁄₃πr³, A = 4πr². Cylinder: V = πr²h, A = 2πr(r+h). Cone: V = ⅓πr²h, A = πr(r+√(r²+h²)). Cube: V = s³, A = 6s². Rectangular prism: V = lwh, A = 2(lw+lh+wh).

Volume is a 3D measure (units³); surface area is a 2D measure (units²). The cone's surface area includes both the circular base (πr²) and the lateral surface (πr·slant_height where slant = √(r²+h²)). The cylinder's lateral surface unrolls into a rectangle of width 2πr and height h. The sphere is unique — it has the smallest surface area for a given volume of any 3D shape, which is why bubbles are spherical (minimizing surface tension energy).

Solid Volume & Surface Area — Reference Formulas

Side-by-side formulas for the five common 3D solids.

Solid	Volume	Surface area	Notes
Sphere (radius r)	⁴⁄₃ π r³	4 π r²	Minimum surface area for given volume
Cylinder (r, h)	π r² h	2 π r (r + h)	Lateral surface = 2πrh; bases = 2πr²
Cone (r, h)	⅓ π r² h	π r (r + ℓ), ℓ = √(r²+h²)	Volume = ⅓ of cylinder with same r, h
Cube (side s)	s³	6 s²	Maximum volume for given surface area among rectangular shapes
Rectangular prism (l, w, h)	l × w × h	2 (lw + lh + wh)	All cuboids; cube is a special case

Practical Examples

Water tank: cylindrical tank with r=1m, h=2m holds π·1²·2 ≈ 6,283 litres (≈ 6.28 m³).

Concrete pour: rectangular foundation 10m × 5m × 0.3m needs 15 m³ of concrete.

Soccer ball: a regulation size 5 ball with circumference 70cm has r=11.14cm, V = 5,793 cm³.

Ice cream cone: a cone with r=3cm, h=12cm holds V = ⅓π·9·12 = 113 cm³ (1 typical scoop).

Sphere vs cube of equal side/diameter: the sphere holds 52% of the cube's volume but has 80% of its surface area.

Frequently Asked Questions

Nine times out of ten, it's a units mismatch. If you put the radius in centimeters and the height in meters, the answer is mathematical nonsense — the calculator just multiplies whatever you hand it. Stay consistent within a single calculation: all cm, or all meters, or all feet. The calculator doesn't unit-check for you; that part is on the human.

Popular Conversions

Jump to a ready-made conversion — useful for quick reference and sharing:

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Premium Converters

3D Solid Volume Calculator

Math

Volume + surface area for sphere, cylinder, cone, cube, and rectangular prism. Interactive 3D visualization — rotate and zoom.

Math

3D Solid Volume Calculator

Generated on May 23, 2026

Shape

Radius (r)

Save / share— download or share to WhatsApp, Facebook & more

Premium Converters

Sphere Volume & Surface Area

V = 523.5988 units³ · A = 314.1593 units²

Generated

5/23/2026

Results

Volume

523.5988

cubic units (units³)

Surface area

314.1593

square units (units²)

Formula

V = ⁴⁄₃ π r³, A = 4 π r²

Loading 3D viewer…

💡 Click and drag the 3D shape to rotate it. Scroll to zoom.

Step-by-step calculation

Formula

V = ⁴⁄₃ π r³, A = 4 π r²

1Shape: Sphere
2r = 5. V = (4/3)π·5³ = 523.5988 units³.
3Surface area = 314.1593 square units.
4Units are unspecified — if your inputs are in cm the volume is in cm³, if in m then m³, etc.

Quick Answer

Volume + surface area for sphere, cylinder, cone, cube, and rectangular prism. Interactive 3D visualization — rotate and zoom.

Overview — 3D Solid Volume Calculator

Math

Formula

Sphere: V = ⁴⁄₃πr³, A = 4πr². Cylinder: V = πr²h, A = 2πr(r+h). Cone: V = ⅓πr²h, A = πr(r+√(r²+h²)). Cube: V = s³, A = 6s². Rectangular prism: V = lwh, A = 2(lw+lh+wh).

By Muhammad Salman SaleemUpdated: May 23, 2026MethodologyFree, no sign-upRuns in your browser — your data stays private

From the editors — what to know before you start

Pro tips most people learn the hard way

Unit consistency is the silent killer. Putting radius in cm and height in m gives you a volume that looks like a real number but is total nonsense. Always stay within one unit system across a single calculation. The most common 'why does my answer look wrong' question on volume problems is always this.
A cone holds exactly one-third the volume of a cylinder with the same radius and height. So if you're scaling a recipe from a cylindrical tank to a conical hopper, multiply by 3 (cone to cylinder) or divide by 3 (cylinder to cone). This 1/3 relationship is true for any pyramid relative to its containing prism — beautiful piece of geometry.
Spheres minimize surface area for a given volume — that's why bubbles, raindrops, and ball bearings naturally form spheres. Conversely, cubes maximize volume for a given surface area among rectangular shapes (it's why suburban warehouses tend toward cubic proportions — most stored volume per dollar of wall and roof).
For real construction calculations, always pad your volume estimate by 5-10 percent for waste, spillage, and edge effects. A concrete pour that calculates to 15 cubic meters should be ordered as 16 to be safe. Running out mid-pour is much worse than having a little extra; the math is mathematically exact but the world is messy.
Surface area matters for cost almost as much as volume. Painting a cylinder, cladding a building, plating a sphere — all charge per unit area. A sphere of diameter 2 m has 12.57 m² of surface; a cube of side 2 m has 24 m². If the contents matter, calculate volume; if the wrapping matters, calculate surface area.

?What is the 3D Solid Volume Calculator?

The Formula

Sphere: V = ⁴⁄₃πr³, A = 4πr². Cylinder: V = πr²h, A = 2πr(r+h). Cone: V = ⅓πr²h, A = πr(r+√(r²+h²)). Cube: V = s³, A = 6s². Rectangular prism: V = lwh, A = 2(lw+lh+wh).

Solid Volume & Surface Area — Reference Formulas

Side-by-side formulas for the five common 3D solids.

Solid	Volume	Surface area	Notes
Sphere (radius r)	⁴⁄₃ π r³	4 π r²	Minimum surface area for given volume
Cylinder (r, h)	π r² h	2 π r (r + h)	Lateral surface = 2πrh; bases = 2πr²
Cone (r, h)	⅓ π r² h	π r (r + ℓ), ℓ = √(r²+h²)	Volume = ⅓ of cylinder with same r, h
Cube (side s)	s³	6 s²	Maximum volume for given surface area among rectangular shapes
Rectangular prism (l, w, h)	l × w × h	2 (lw + lh + wh)	All cuboids; cube is a special case

Practical Examples

Water tank: cylindrical tank with r=1m, h=2m holds π·1²·2 ≈ 6,283 litres (≈ 6.28 m³).

Concrete pour: rectangular foundation 10m × 5m × 0.3m needs 15 m³ of concrete.

Soccer ball: a regulation size 5 ball with circumference 70cm has r=11.14cm, V = 5,793 cm³.

Ice cream cone: a cone with r=3cm, h=12cm holds V = ⅓π·9·12 = 113 cm³ (1 typical scoop).

Sphere vs cube of equal side/diameter: the sphere holds 52% of the cube's volume but has 80% of its surface area.

Frequently Asked Questions

Popular Conversions

Jump to a ready-made conversion — useful for quick reference and sharing:

Browse all Math

GPA Calculator

Calculate your semester or cumulative Grade Point Average on the 4.0 scale, weighted by credit hours, with support for both weighted and unweighted grading systems.

Grade Calculator

Calculate your final grade from weighted categories like tests, homework, and exams.

Student Result Card Calculator

Subject-wise marks, grades, and a printable school result card — ideal for small schools and parents.

Fraction Calculator

Add, subtract, multiply, and divide proper, improper, and mixed fractions with automatic reduction to lowest terms and decimal equivalents for cooking, carpentry, and homework.

Ratio Calculator

Simplify ratios to lowest terms using GCD and solve proportions like a:b = c:x for any missing value — useful for recipes, map scales, aspect ratios, and mixing ingredients.

Average Calculator

Compute the arithmetic mean, median, mode, range, count, sum, minimum, and maximum from any list of numbers — essential for descriptive statistics, surveys, and grading.

LCM / GCD Calculator

Find the LCM and GCD (HCF) of two or more integers using the Euclidean algorithm — useful for simplifying fractions, finding common denominators, and scheduling repeating events.

Prime Number Checker

Test whether any integer is a prime number using trial division up to its square root, and view the complete unique prime factorization for composite numbers.

Browse all Math calculators & converters

See every tool in this category, plus FAQs and category-specific guides.

Browse other categories

Islamic9 Financial14 Gold & Silver8 Health25 Unit19 Date & Time9 Construction22 Utility20 Fun12

3D Solid Volume Calculator — Volume + surface area for sphere | Premium Converters

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Premium Converters

3D Solid Volume Calculator

3D Solid Volume Calculator

Sphere Volume & Surface Area

Step-by-step calculation

Overview — 3D Solid Volume Calculator

From the editors — what to know before you start

Pro tips most people learn the hard way

?What is the 3D Solid Volume Calculator?

The Formula

Solid Volume & Surface Area — Reference Formulas

Practical Examples

Frequently Asked Questions

Popular Conversions

Embed this calculator on your site

Browse other categories

Premium Converters

3D Solid Volume Calculator

3D Solid Volume Calculator

Sphere Volume & Surface Area

Step-by-step calculation

Overview — 3D Solid Volume Calculator

From the editors — what to know before you start

Pro tips most people learn the hard way

?What is the 3D Solid Volume Calculator?

The Formula

Solid Volume & Surface Area — Reference Formulas

Practical Examples

Frequently Asked Questions

Popular Conversions

Embed this calculator on your site

Browse other categories

Premium Converters

Premium Converters

3D Solid Volume Calculator

3D Solid Volume Calculator

Step-by-step calculation

Overview — 3D Solid Volume Calculator

From the editors — what to know before you start

Pro tips most people learn the hard way

?What is the 3D Solid Volume Calculator?

The Formula

Solid Volume & Surface Area — Reference Formulas

Practical Examples

Frequently Asked Questions

Why does my cylinder volume look wrong?

Can I rotate the 3D shape?

Why isn't there a triangular prism?

Does the calculator use π = 3.14 or full precision?

Popular Conversions

Embed this calculator on your site

More Math Tools

Browse other categories

Premium Converters

3D Solid Volume Calculator

3D Solid Volume Calculator

Step-by-step calculation

Overview — 3D Solid Volume Calculator

From the editors — what to know before you start

Pro tips most people learn the hard way

?What is the 3D Solid Volume Calculator?

The Formula

Solid Volume & Surface Area — Reference Formulas

Practical Examples

Frequently Asked Questions

Why does my cylinder volume look wrong?

Can I rotate the 3D shape?

Why isn't there a triangular prism?

Does the calculator use π = 3.14 or full precision?

Popular Conversions

Embed this calculator on your site

More Math Tools

Browse other categories