Volume of Torus Calculator

✖Radius of Torus is the line connecting the center of the overall Torus to the center of a circular cross-section of the Torus.ⓘ Radius of Torus [r]			+10% -10%
✖Radius of Circular Section of Torus is the line connecting the center of the circular cross section to any point on the circumference of the circular cross section of the Torus.ⓘ Radius of Circular Section of Torus [r_{Circular Section}]			+10% -10%

✖Volume of Torus is the amount of three dimensional space occupied by Torus.ⓘ Volume of Torus [V]

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Formula

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Volume of Torus

Formula

`"V" = 2*(pi^2)*"r"*("r"_{"Circular Section"}^2)`

Example

`"12633.09m³"=2*(pi^2)*"10m"*(("8m")^2)`

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Volume of Torus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Torus = 2*(pi^2)*Radius of Torus*(Radius of Circular Section of Torus^2)
V = 2*(pi^2)*r*(r_{Circular Section}^2)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Torus - (Measured in Cubic Meter) - Volume of Torus is the amount of three dimensional space occupied by Torus.
Radius of Torus - (Measured in Meter) - Radius of Torus is the line connecting the center of the overall Torus to the center of a circular cross-section of the Torus.
Radius of Circular Section of Torus - (Measured in Meter) - Radius of Circular Section of Torus is the line connecting the center of the circular cross section to any point on the circumference of the circular cross section of the Torus.

STEP 1: Convert Input(s) to Base Unit

Radius of Torus: 10 Meter --> 10 Meter No Conversion Required
Radius of Circular Section of Torus: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 2*(pi^2)*r*(r_{Circular Section}^2) --> 2*(pi^2)*10*(8^2)

Evaluating ... ...

V = 12633.0936333944

STEP 3: Convert Result to Output's Unit

12633.0936333944 Cubic Meter --> No Conversion Required

FINAL ANSWER

12633.0936333944 ≈ 12633.09 Cubic Meter <-- Volume of Torus

(Calculation completed in 00.004 seconds)

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Created by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< 8 Volume of Torus Calculators

Volume of Torus given Radius of Circular Section and Total Surface Area

Go Volume of Torus = (2*(pi^2)*(Radius of Circular Section of Torus^2)*(Total Surface Area of Torus/(4*pi^2*Radius of Circular Section of Torus)))

Volume of Torus given Radius of Circular Section and Hole Radius

Go Volume of Torus = (2*(pi^2)*(Radius of Circular Section of Torus^2)*(Hole Radius of Torus+Radius of Circular Section of Torus))

Volume of Torus given Radius of Circular Section and Breadth

Go Volume of Torus = (2*(pi^2)*(Radius of Circular Section of Torus^2)*((Breadth of Torus/2)-Radius of Circular Section of Torus))

Volume of Torus given Radius and Total Surface Area

Go Volume of Torus = (2*(pi^2)*(Radius of Torus)*((Total Surface Area of Torus/(4*(pi^2)*Radius of Torus))^2))

Volume of Torus given Radius and Hole Radius

Go Volume of Torus = (2*(pi^2)*(Radius of Torus)*((Radius of Torus-Hole Radius of Torus)^2))

Volume of Torus given Radius and Breadth

Go Volume of Torus = (2*(pi^2)*(Radius of Torus)*(((Breadth of Torus/2)-Radius of Torus)^2))

Volume of Torus given Radius and Surface to Volume Ratio

Go Volume of Torus = (2*(pi^2)*(Radius of Torus)*((2/Surface to Volume Ratio of Torus)^2))

Volume of Torus

Go Volume of Torus = 2*(pi^2)*Radius of Torus*(Radius of Circular Section of Torus^2)

< 4 Volume of Torus Calculators

Volume of Torus given Radius of Circular Section and Hole Radius

Go Volume of Torus = (2*(pi^2)*(Radius of Circular Section of Torus^2)*(Hole Radius of Torus+Radius of Circular Section of Torus))

Volume of Torus given Radius and Hole Radius

Go Volume of Torus = (2*(pi^2)*(Radius of Torus)*((Radius of Torus-Hole Radius of Torus)^2))

Volume of Torus given Radius and Breadth

Go Volume of Torus = (2*(pi^2)*(Radius of Torus)*(((Breadth of Torus/2)-Radius of Torus)^2))

Volume of Torus

Go Volume of Torus = 2*(pi^2)*Radius of Torus*(Radius of Circular Section of Torus^2)

Volume of Torus Formula

Volume of Torus = 2*(pi^2)*Radius of Torus*(Radius of Circular Section of Torus^2)
V = 2*(pi^2)*r*(r_{Circular Section}^2)

What is Torus?

In geometry, a Torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.

If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is a related shape, a toroid.

How to Calculate Volume of Torus?

Volume of Torus calculator uses Volume of Torus = 2*(pi^2)*Radius of Torus*(Radius of Circular Section of Torus^2) to calculate the Volume of Torus, The Volume of Torus formula is defined as the amount of three dimensional space occupied by Torus. Volume of Torus is denoted by V symbol.

How to calculate Volume of Torus using this online calculator? To use this online calculator for Volume of Torus, enter Radius of Torus (r) & Radius of Circular Section of Torus (r_{Circular Section}) and hit the calculate button. Here is how the Volume of Torus calculation can be explained with given input values -> 12633.09 = 2*(pi^2)*10*(8^2).

FAQ

What is Volume of Torus?

The Volume of Torus formula is defined as the amount of three dimensional space occupied by Torus and is represented as V = 2*(pi^2)*r*(r_{Circular Section}^2) or Volume of Torus = 2*(pi^2)*Radius of Torus*(Radius of Circular Section of Torus^2). Radius of Torus is the line connecting the center of the overall Torus to the center of a circular cross-section of the Torus & Radius of Circular Section of Torus is the line connecting the center of the circular cross section to any point on the circumference of the circular cross section of the Torus.

How to calculate Volume of Torus?

The Volume of Torus formula is defined as the amount of three dimensional space occupied by Torus is calculated using Volume of Torus = 2*(pi^2)*Radius of Torus*(Radius of Circular Section of Torus^2). To calculate Volume of Torus, you need Radius of Torus (r) & Radius of Circular Section of Torus (r_{Circular Section}). With our tool, you need to enter the respective value for Radius of Torus & Radius of Circular Section of Torus and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Torus?

In this formula, Volume of Torus uses Radius of Torus & Radius of Circular Section of Torus. We can use 10 other way(s) to calculate the same, which is/are as follows -

Volume of Torus = (2*(pi^2)*(Radius of Circular Section of Torus^2)*(Hole Radius of Torus+Radius of Circular Section of Torus))
Volume of Torus = (2*(pi^2)*(Radius of Circular Section of Torus^2)*((Breadth of Torus/2)-Radius of Circular Section of Torus))
Volume of Torus = (2*(pi^2)*(Radius of Torus)*((Radius of Torus-Hole Radius of Torus)^2))
Volume of Torus = (2*(pi^2)*(Radius of Torus)*(((Breadth of Torus/2)-Radius of Torus)^2))
Volume of Torus = (2*(pi^2)*(Radius of Torus)*((2/Surface to Volume Ratio of Torus)^2))
Volume of Torus = (2*(pi^2)*(Radius of Circular Section of Torus^2)*(Total Surface Area of Torus/(4*pi^2*Radius of Circular Section of Torus)))
Volume of Torus = (2*(pi^2)*(Radius of Torus)*((Total Surface Area of Torus/(4*(pi^2)*Radius of Torus))^2))
Volume of Torus = (2*(pi^2)*(Radius of Torus)*(((Breadth of Torus/2)-Radius of Torus)^2))
Volume of Torus = (2*(pi^2)*(Radius of Torus)*((Radius of Torus-Hole Radius of Torus)^2))
Volume of Torus = (2*(pi^2)*(Radius of Circular Section of Torus^2)*(Hole Radius of Torus+Radius of Circular Section of Torus))

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