Formula Reference
Volume Formulas — All Shapes
Click any shape to open that calculator with pre-loaded fields. Covers cylinder, cone, sphere, pyramid, triangular prism, and more.
Free online volume calculator for any shape or container. Cylinder, cone, sphere, pyramid, triangular prism, tank, pipe, pool, aquarium, pond, concrete, and medical volumes. Full formula and steps every time.
Click any shape to open that calculator with pre-loaded fields. Covers cylinder, cone, sphere, pyramid, triangular prism, and more.
Our volume calculator covers construction, engineering, aquatics, plumbing, cooking, farming, and medical applications.
Find how many gallons your swimming pool holds. Rectangular pool uses box formula; circular pool uses cylinder volume calculator. Results in gallons and litres.
Calculate liquid volume in horizontal or vertical cylindrical tanks, rectangular tanks, or oval tanks. Used for fuel, water, septic, and chemical storage tanks.
Calculate how much liquid a pipe holds using inner diameter and length. Essential for plumbing, hydraulics, and calculating water volume in pipeline systems.
Calculate cubic yards or cubic meters of concrete needed for slabs, columns, footings, and walls. Rectangular prism formula for slabs; cylinder formula for round columns.
Find the volume of your fish tank in gallons or litres to buy the right filter, heater, and determine fish capacity. Use the rectangular box or cylinder formula.
Calculate prostate volume using the ellipsoid formula, bladder volume, and tidal volume reference values. Used by clinicians for diagnosis and dosage calculations.
This volume calculator covers every type of volume calculation you will ever need — from basic geometric shapes like cylinders, cones, spheres, pyramids, and triangular prisms to practical container volumes for pools, tanks, pipes, aquariums, ponds, and specialty calculations including concrete volume and medical volumes for prostate, bladder, and tidal volume. Every result shows the formula with your values substituted in, step-by-step working, and automatic conversions to litres, US gallons, and other common units.
The cylinder volume calculator uses the formula V = pi x r2 x h. This is the most commonly used volume formula because cylinders appear everywhere — water tanks, pipes, cans, wells, columns, and pools. If you know the diameter instead of the radius, divide by 2 first.
Tank with diameter 6 ft and height 8 ft: r = 3 ft, V = pi x 9 x 8 = 226.19 ft3 = 1,691.6 gallons = 6,404 litres
The cone volume calculator uses V = (1/3) x pi x r2 x h. A cone always holds exactly one-third the volume of a cylinder with the same base radius and height. Use this for grain silos, hoppers, traffic cones, and ice cream cone volumes.
The sphere volume calculator uses V = (4/3) x pi x r3. Volume increases with the cube of the radius — so doubling the radius increases volume by 8 times. Common applications include balls, globes, spherical tanks, and gas storage spheres.
A triangular prism volume calculator uses V = (1/2) x base x height x length. Enter the base and height of the triangular cross-section, then the length (depth) of the prism. Used for roof volumes, Toblerone-shaped packaging, and drainage channels with triangular cross-sections.
To use our pool volume calculator, identify your pool shape first. A rectangular pool uses the box formula: V = L x W x D. A round (circular) pool uses the cylinder formula: V = pi x r2 x depth. All results automatically convert to US gallons so you can calculate chlorine and chemical dosages correctly.
Pool 30 ft x 15 ft x 5 ft deep: V = 30 x 15 x 5 = 2,250 ft3 = 16,832 US gallons = 63,706 litres
Our tank volume calculator handles both cylindrical tanks (vertical and horizontal) and rectangular tanks. For a horizontal cylindrical tank, the formula depends on the fill level, which our calculator handles automatically. Tank volumes are used for fuel oil, water storage, chemical processing, and septic systems.
The pipe volume calculator uses the same cylinder formula but applies it to the inner diameter: V = pi x (inner radius)2 x length. Important: always use the inner diameter, not the outer diameter, for liquid volume calculations. This is essential for plumbing, irrigation design, and fire suppression system calculations.
Pipe with 4-inch inner diameter and 100 ft long: r = 2 in = 0.1667 ft, V = pi x 0.02778 x 100 = 8.73 ft3 = 65.3 gallons of water
To find your aquarium volume, use the rectangular box formula for standard fish tanks: V = L x W x H. For a cylindrical aquarium, use the cylinder formula. A standard 40-gallon tank is approximately 36 x 18 x 16 inches. Knowing exact volume helps determine the correct filter flow rate, heater wattage, and safe fish stocking levels.
Pond volume depends on the pond shape. A rectangular pond uses V = L x W x average depth. An oval or kidney-shaped pond can be approximated using the ellipsoid or cylinder formula with average dimensions. Pond volume is critical for calculating fish stocking density, water treatment dosages, and pump sizing for circulation and aeration.
Any container volume can be converted to a water volume or liquid volume automatically using our conversion chips. Key conversions: 1 ft3 = 7.481 US gallons = 28.317 litres. 1 m3 = 1,000 litres = 264.2 US gallons. 1 US gallon = 3.785 litres = 231 in3.
Our concrete volume calculator uses the rectangular prism formula for slabs and the cylinder formula for round columns. Results are shown in cubic feet and automatically converted to cubic yards (divide ft3 by 27) since ready-mix concrete is sold by the cubic yard in the US.
Driveway 20 ft x 10 ft x 0.33 ft (4 inches) thick: V = 66 ft3 = 2.44 cubic yards. Order at least 2.7 yards to include 10% waste.
The prostate volume calculator uses the prolate ellipsoid formula: V = 0.52 x length x width x height (all dimensions in centimeters, result in mL). Measurements are obtained from transrectal ultrasound (TRUS) or MRI. Normal prostate volume is 20–30 mL. Values above 30 mL may indicate benign prostatic hyperplasia (BPH).
| Volume Range | Interpretation | PSA Density Context |
|---|---|---|
| Less than 20 mL | Small/normal prostate | Normal range |
| 20–30 mL | Normal adult prostate | Expected for age 40–60 |
| 30–50 mL | Mildly enlarged | May cause mild BPH symptoms |
| Greater than 50 mL | Significantly enlarged | Likely BPH, may affect treatment choice |
Note: Prostate volume results are for reference only. Always consult a qualified urologist for clinical interpretation and treatment decisions.
The bladder volume calculator uses the ellipsoid formula: V = 0.52 x length x width x height (from ultrasound measurements in cm, result in mL). Normal bladder capacity is 300–500 mL. Post-void residual (PVR) volume above 100 mL may indicate urinary retention. Maximum cystometric capacity averages 400–600 mL in adults.
| Bladder Volume | Clinical Significance |
|---|---|
| 0–50 mL PVR | Normal post-void residual |
| 50–100 mL PVR | Borderline — may need monitoring |
| 100–200 mL PVR | Clinically significant retention |
| Greater than 200 mL PVR | High residual — requires clinical evaluation |
| 300–500 mL full | Normal functional capacity |
Tidal volume is the amount of air moved in or out of the lungs during each normal, relaxed breath. It is calculated using the formula: Tidal Volume = 6–8 mL x Ideal Body Weight (kg). Average adult tidal volume is approximately 500 mL (0.5 litres) at rest. This value is critical for setting mechanical ventilator parameters.
| Population | Normal Tidal Volume | Notes |
|---|---|---|
| Adult male | 500–600 mL | 6–8 mL/kg ideal body weight |
| Adult female | 400–500 mL | 6–8 mL/kg ideal body weight |
| Child (5 years) | 150–200 mL | ~7 mL/kg body weight |
| Infant | 15–25 mL | 6–8 mL/kg body weight |
| Ventilated patient | 6 mL/kg IBW | ARDSnet lung-protective strategy |
Medical Disclaimer: Tidal volume, prostate volume, and bladder volume calculators are for educational and reference purposes only. They do not replace professional clinical assessment, imaging interpretation, or medical advice from a qualified healthcare provider.
Volume Unit Conversions: 1 m3 = 1,000 litres = 264.2 US gallons. 1 ft3 = 7.481 gallons = 28.317 litres. 1 UK gallon = 4.546 litres. 1 US gallon = 3.785 litres = 231 in3. 1 cm3 = 1 mL. 1 litre = 1,000 mL = 61.02 in3. Our calculator shows all relevant conversions automatically after each calculation.
Use the cylinder volume formula: V = pi x r2 x h where r is the radius (half the diameter) and h is the height or length. Example: a cylinder with diameter 6 ft and height 8 ft has r = 3 ft, so V = pi x 9 x 8 = 226.19 ft3 = 1,692 gallons. This same formula works for pipe volume, tank volume, and circular pool volume.
For a rectangular pool: Volume (ft3) = Length x Width x Average Depth, then multiply by 7.481 for US gallons. For a round pool: V = pi x r2 x depth x 7.481. Example: a 25 ft x 12 ft x 5 ft pool = 1,500 ft3 = 11,221 gallons. Select Pool in our Containers tab for an instant result with gallons and litres shown automatically.
Pipe volume = pi x (inner radius)2 x length. Always use the inner (bore) diameter, not the outside diameter. For a 3-inch inner diameter pipe, 50 feet long: r = 1.5 in = 0.125 ft, V = pi x 0.015625 x 50 = 2.45 ft3 = 18.34 gallons. Use the Pipe option in our Containers tab for step-by-step working.
Calculate volume in cubic feet first (L x W x D in feet), then divide by 27 to convert to cubic yards. Example: a driveway 20 ft x 10 ft x 4 inches thick (0.333 ft): V = 66.7 ft3 / 27 = 2.47 cubic yards. Always add 10% extra for waste and spillage, so order 2.7 yards. Our calculator converts to cubic yards automatically.
Prostate volume is calculated from ultrasound or MRI measurements using the prolate ellipsoid formula: V = 0.52 x length x width x height (in cm, result in mL). A normal prostate is 20–30 mL. Above 30 mL may indicate benign prostatic hyperplasia (BPH). Prostate volume also factors into PSA density calculations, which help distinguish BPH from prostate cancer. Always have results interpreted by a urologist.
Tidal volume is the volume of air moved per breath during normal, relaxed breathing. Normal adult tidal volume is approximately 500 mL (0.5 litres). It is estimated as 6–8 mL per kg of ideal body weight. For mechanically ventilated patients, the ARDSnet protocol recommends 6 mL/kg of predicted body weight to protect lung tissue. Tidal volume is measured during pulmonary function testing or spirometry.