Simple Pendulum Calculator

Simple Pendulum is evaluated from Pendulum Length, Period and Frequency. The calculation reports Period, Frequency and Pendulum Length.

Results

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About the Simple Pendulum Calculator

Simple Pendulum is treated here as a quantitative relation between Pendulum Length, Period and Frequency and Period, Frequency, Pendulum Length and Pendulum Length.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
T = 2pi x sqrt(L / g) - Period in seconds
f = 1 / T - Frequency in Hz
L = g x T^2 / (4pi^2) - Length from period
L = g / (4pi^2 x f^2) - Length from frequency
g = 9.80665 m/s^2

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

T = 2pi x sqrt(L / g) - Period in seconds
f = 1 / T - Frequency in Hz
L = g x T^2 / (4pi^2) - Length from period
L = g / (4pi^2 x f^2) - Length from frequency
g = 9.80665 m/s^2

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Grandfather Clock Pendulum

Inputs

length: 0.9942
Period: 2.0006 s. Frequency: 0.4999 Hz

With Pendulum Length = 0.9942 as the stated inputs, the result is Period = 2.0006 s and Frequency = 0.4999 Hz. Each value corresponds to the declared output fields.

Example 2: Playground Swing — Child's Height

Inputs

length: 2.5
Period: 3.1724 s. Frequency: 0.3152 Hz

With Pendulum Length = 2.5 as the stated inputs, the result is Period = 3.1724 s and Frequency = 0.3152 Hz. Each value corresponds to the declared output fields.

Example 3: Design a 1 Hz Metronome Pendulum

Inputs

frequency: 1
Period: 1 s. Pendulum Length: 0.2484 m. Pendulum Length: 9.78 in

With Frequency = 1 as the stated inputs, the result is Period = 1 s, Pendulum Length = 0.2484 m and Pendulum Length = 9.78 in. Each value corresponds to the declared output fields.

Example 4: Estimating g at a New Location

Inputs

length: 1
Period: 2.0064 s. Frequency: 0.4984 Hz

With Pendulum Length = 1 as the stated inputs, the result is Period = 2.0064 s and Frequency = 0.4984 Hz. Each value corresponds to the declared output fields.

Common Use Cases

  • Design a grandfather clock pendulum for 1-second beats
  • Calculate the period of a playground swing
  • Find the required length for a specific pendulum frequency