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Pendulum Period and Bottom Speed

Calculate pendulum period and bottom speed with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

period = 2.0064093; frequency = 0.4984028; max energy = 0.980665; max speed = 1.4004749. Values use the worked example unit selections.

T = 2Ο€βˆš(β„“/g); f = 1/T; E = mgh; vmax = √(2gh)

Worked example

Enter these known values and leave the other values blank.

Length (L)
1 m
Acceleration of gravity (g)
1 g
Mass (m)
1 kg
Height (h)
0.1 m
Period (T)
2.0064 sec
Frequency (f)
0.4984 Hz
Energy available
0.9807 J
Maximum Speed
1.4005 m/s

Assumptions and limitations

  • Period is a small-angle approximation for an ideal simple pendulum. Starting height is relative to the bottom and no greater than the length. Energy and maximum speed neglect drag and pivot loss.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.

Common questions

What does this calculation assume?

Period is a small-angle approximation for an ideal simple pendulum. Starting height is relative to the bottom and no greater than the length. Energy and maximum speed neglect drag and pivot loss.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Original accessible explanations preserve the captured diagram geometry, quantities and conditional variants without external image loading. Restrict the physical model to non-singular dimensions and stated principal inverse branches; discrete gear/fringe counts are exact integers.

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