The following calculator is designed to calculate the pendulum length based on inputs acceleration due to gravity and Frequency. The tool can make work easy for students and educators.

A pendulum’s length is the distance between the point of suspension and its center of mass. This length determines the period of the swing, which is the time it takes to complete one full oscillation.

**Imputing Guide**

Input | Action |
---|---|

Gravity (g) | Enter gravity in m/s² (e.g., 9.8). |

Frequency (f) | Enter frequency in Hz (e.g., 0.5). |

Pendulum Length (PL) | Enter length in meters if known, or leave blank to calculate. |

Click Calculate | Calculates the unknown value based on inputs. |

**Calculation Examples**

Calculation Type | Example Values |
---|---|

Basic | g = 9.8, f = 0.5 |

Advanced | g = 9.8, f = 0.5, PL = 0.248 |

### Formula for Pendulum Length

Calculate pendulum length with:

$\text{PL} = \frac{g}{4 \cdot \pi^2 \cdot f^2$

Variable | Description |
---|---|

PL | Pendulum Length (meters) |

g | Acceleration due to Gravity (m/s²) |

f | Frequency (Hz) |

**Calculation Example**

Step | Calculation |
---|---|

Gravity (g) | 9.8 m/s² |

Frequency (f) | 0.5 Hz |

Step 1: Square the frequency | $0.5^2 = 0.2$ |

Step 2: Multiply by $4 \cdot \pi^2$ | $4 \cdot (3.142)^2 =$ |

Step 3: Divide gravity by the product | $\frac{9.8}{39.48}$m |

**Answer:** The pendulum length is approximately 0.248 meters.