Moment of Inertia Calculator

The Moment of Inertia Calculator will calculate:

Moment of Inertia of a bar rotating around its centre
Moment of Inertia of a bar rotating around its end
Moment of Inertia of a cylinder or disc rotating around its axis of symmetry
Moment of Inertia of a cylinder or disc rotating around its central diameter
Moment of Inertia of a ring rotating around its axis of symmetry
Moment of Inertia of a ring rotating around its diameter
Moment of Inertia of a sphere rotating around its diameter
Moment of Inertia of a spherical shell rotating around its diameter
Moment of Inertia of a point object rotating around a given axis

Moment of Inertia Calculator
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Calculator Precision (Decimal Places)
Mass of bar (m_b) kg
Length of bar (L) m
Mass of cylinder or disc (m_C) kg
Radius of cylinder or disc (R_C) m
Height of cylinder (h) m
Mass of ring (m_R) kg
Outer radius of ring (R_R) m
Mass of sphere (m_S) kg
Radius of sphere (R_S) m
Mass of spherical shell (m_Sh) kg
Radius of spherical shell (R_Sh) m
Mass of the point object (m_ob) kg
Distance of the point object from the rotation axis(r) m

Moment of Inertia Calculator Results (detailed calculations and formula below)
Moment of inertia of a bar rotating around its centre calculation
The Moment of inertia of a bar rotating around its centre calculation is kg∙m²
The Moment of Inertia of a bar rotating around its end is kg∙m²
The Moment of Inertia of a cylinder or disc rotating around its axis of symmetry is kg∙m²
The Moment of Inertia of a cylinder or disc rotating around its central diameter is kg∙m²
The Moment of Inertia of a ring rotating around its axis of symmetry is kg∙m²
The Moment of Inertia of a ring rotating around its diameter is kg∙m²
The Moment of Inertia of a sphere rotating around its diameter is kg∙m²
The Moment of Inertia of a spherical shell rotating around its diameter is kg∙m²
The Moment of Inertia of a point object rotating around a given axis is kg∙m²
I = 1/12 × m_b × L² I = 1/12 × × ² I = × × I =
Moment of inertia of a bar rotating around its end calculation
I = 1/3 × m_b × L² I = 1/3 × × ² I = × × I =
Moment of Inertia of a cylinder or disc rotating around its axis of symmetry calculation
I = 1/2 × m_C × R_C² I = 1/2 × × ² I = × × I =
Moment of Inertia of a cylinder or disc rotating around its central diameter calculation
I = 1/4m_C × R_C² + 1/12m_C × h² I = 1/4 × ² + 1/12 × ² I = × × + × × I =
Moment of Inertia of a ring rotating around its axis of symmetry calculation
I = m_R × R_R² I = × ² I = × I =
Moment of Inertia of a ring rotating around its diameter calculation
I = 1/2m_R × R_R² I = 1/2 × ² I = × × I =
Moment of Inertia of a sphere rotating around its diameter calculation
I = 2/5m_S × R_S² I = 2/5 × ² I = × × I =
Moment of Inertia of a spherical shell rotating around its diameter calculation
I = 2/3m_Sh × R_Sh² I = 2/3 × ² I = × × I =
Moment of Inertia of a point object rotating around a given axis calculation
I = m_obj × r² I = × ² I = × I =
Moment Of Inertia Calculator Input Values
Mass of bar (mb) kg
Length of bar (L) m
Mass of cylinder or disc (mC) kg
Radius of cylinder or disc (RC) m
Height of cylinder (h) m
Mass of ring (mR) kg
Outer radius of ring (RR) m
Mass of sphere (mS) kg
Radius of sphere (RS) m
Mass of spherical shell (mSh) kg
Radius of spherical shell (RSh) m
Mass of the point object (mob) kg
Distance of the point object from the rotation axis(r) m

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each moment of inertia calculation, the Moment Of Inertia Calculator will automatically calculate the results and update the Physics formula elements with each element of the moment of inertia calculation. You can then email or print this moment of inertia calculation as required for later use.

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Discover Physics with free Physics Revision Notes and Physics Calculator: Moment Of Inertia. This image shows the properties and moment of inertia formula for the Moment Of Inertia. This calculator will calculate the Moment of Inertia of a bar rotating around its centre and rotating around its end, a cylinder or disc rotating around its axis of symmetry, a ring rotating around its diameter and more

Moment of Inertia of a bar rotating around its centre Formula and Calculation

I = 1/12 × m_b × L²

Moment of Inertia of a bar rotating around its end Formula and Calculation

I = 1/3 × m_b × L²

Moment of Inertia of a cylinder or disc rotating around its axis of symmetry Formula and Calculation

I = 1/2 × m_C × R_C²

Moment of Inertia of a cylinder or disc rotating around its central diameter Formula and Calculation

I = 1/4m_C × R_C² + 1/m12_C × h²

The Moment of Inertia of a ring rotating around its axis of symmetry Formula and Calculation

I = m_R × R_R²

The Moment of Inertia of a ring rotating around its diameter Formula and Calculation

I = 1/2m_R × R_R²

Moment of Inertia of a sphere rotating around its diameter Formula and Calculation

I = 2/5m_S × R_S²

Moment of Inertia of a spherical shell rotating around its diameter Formula and Calculation

I = 2/3m_Sh × R_Sh²

Moment of Inertia of a point object rotating around a given axis Formula and Calculation

I = m_obj × r²

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