Welcome to the Physics library, here we have calculations and content for general physics concepts all the way through to topic areas like fluid mechanics and thermodynamics!

Moment of Inertia Calculators

Physics Calculations

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With this equation, the moments of inertia of a composite shape, which is made up of multiple elementary shapes, can be found. The moment of inertia of each individual shape about its own centroidal axis is found first; then, the parallel axis terms are added to determine the moment of inertia of the composite area.  

For composite shapes made up of smaller shapes or subparts, the moment of inertia for the entire cross-section is equivalent to the sum of the moments of inertia of the individual shapes, 1, 2 and 3, about the global N.A. in the diagram shown here.

If there are any holes or voids within the cross sections, their moment of inertia must also be calculated but subtracted from the total. 

Calculate moment of inertia for any shape with our Free-To-Use Moment of Inertia Calculators. Accurate results in seconds - Join our community today

This calculation tool is designed to help you quickly and accurately determine the slenderness ratio. 

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The slenderness ratio or slenderness is the ratio of effective length to the least radius of gyration and it is calculated using the formula 

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Slenderness Ratio Calculator

🏁 CalcTree's Free-To-Use Slenderness Ratio Calculator helps you determine the critical load of your column. Get quick results without any costs!

This page provides some insight into determining the strain, and provides some functions to help you calculate it!

Strain is the amount of deformation experienced by the body in the direction of force applied i.e. due to stress. It is defined as the ratio of change in shape to its original shape. The following equation determines the relation for deformation in terms of the length of a solid

Strain Calculator

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This page provides some insight into determining stress, and provides some functions to help you calculate it!

Stress is defined as a force that changes the shape of an object. The units of stress are Pascals (Pa) or Newton per square metre (N/m^2), and is calculated according to the following formula

Stress Calculator

🏁 Use CalcTree's Free-To-Use Stress Calculator to determine the stress and strain of any object. Get accurate results in seconds without any costs! 💡

This calculation tool is designed to help you quickly and accurately determine the hydraulic depth of a flowing body of water.

The Froude number, Fr, is a dimensionless value that describes different flow regimes of open channel flow. The Froude number is a ratio of inertial and gravitational forces.

It's used in fluid dynamics to measure the relative importance of gravity and inertia forces in a flow.  The Froude Number can range from 0 to infinity, with 0 representing a flow with no inertia and infinity representing a flow with no gravity.

The Froude number is calculated as the ratio of the inertial force of the flow to the gravitational force of the flow.

The hydraulic depth can be solved by rearranging the formula to solve for flow depth. This is shown below:

Froude Number Calculator (Open Channel Flow)

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Bernoulli Equation Calculator | Calculate Volume Flow Rate

Bernoulli Equation Calculator | Calculate Mass Flow Rate

Bernoulli Calculator

Free-To-Use Bernoulli Equation Calculator: Calculate Mass Flow Rate for Fluid Mechanics Problems with Ease. Simplify Your Work with CalcTree!

This template explores Hooke's Law both in general terms, and in the context of spring constants, it's most common usage.

Hooke's law can of course be rearranged to solve for each variable. Below presents a calculation to solve for F. Remember to account for the direction of your deflection and units...

Go ahead and duplicate this page to change it up and solve for k or s!

Hooke's law states that the strain/deformation of an elastic object or material is proportional to the stress applied to it. 

In this context, Hooke's Law is expressed as:

Hooke's Law

🏁 CalcTree's Free-to-use Hooke's Law Calculator to determine the force needed to extend or compress a spring. Input calculation values. Start now 💡

General

Fluid Mechanics