This **decibel distance calculator** is used to **calculate** how the **sound pressure level (SPL)** changes as you move **closer** or **farther** away from the source.

The calculator typically requires you to input the **initial sound level** (in decibels), the **initial distance**, and either the **final distance** or the **final sound level**. It then uses the **inverse square law** to calculate the missing value, which is the final sound level or distance.

When you know that a sound source has an initial level of **100 dB** at a distance of **1 meter**, and you want to find the sound level at **2 meters**, you can input these values into the calculator. It will then use the formula to determine that the sound level at **2 meters** is approximately **94 dB**.

## Decibel Distance Calculator

Initial Distance (m) | Initial Sound Level (dB) | Final Distance (m) | Final Sound Level (dB) |
---|---|---|---|

1 | 100 | 2 | 94.0 |

1 | 100 | 5 | 86.0 |

1 | 100 | 10 | 80.0 |

1 | 100 | 20 | 74.0 |

2 | 94 | 4 | 88.0 |

2 | 94 | 6 | 84.0 |

2 | 94 | 10 | 80.0 |

2 | 94 | 15 | 76.0 |

5 | 85 | 10 | 79.0 |

5 | 85 | 15 | 76.0 |

5 | 85 | 20 | 73.0 |

5 | 85 | 30 | 70.0 |

10 | 80 | 20 | 74.0 |

10 | 80 | 30 | 71.0 |

10 | 80 | 50 | 67.0 |

10 | 80 | 100 | 64.0 |

15 | 78 | 30 | 72.0 |

15 | 78 | 50 | 69.0 |

15 | 78 | 75 | 66.0 |

15 | 78 | 100 | 63.0 |

20 | 75 | 40 | 69.0 |

20 | 75 | 60 | 66.0 |

20 | 75 | 80 | 63.0 |

20 | 75 | 100 | 60.0 |

## Decibel Distance Calculation Formula

**L2 = L1 - 20 log10(d2/d1)**

Where:

L1is the initial sound level (in decibels)d1is the initial distance from the sourceL2is the final sound level (in decibels)d2is the final distance from the source

Given a sound source producing **100 dB** at **1 meter**, calculate the sound level at **10 meters**:

L2 = 100 – 20

log10(10 / 1)1

L2 = 100 – 20

L2 =80 dB

This formula demonstrates that for every **doubling of distance**, the sound level decreases by approximately **6 dB** in **free-field conditions**.

To use this formula, you need to know **three out of the four variables**. If you know the initial sound level (**L1**), the initial distance (**d1**), and the final distance (**d2**), you can calculate the final sound level (**L2**) using the formula.

## How to Calculate Decibels at Distance?

**Determine the initial sound level**(in decibels) and the initial distance from the source.**Decide on the final distance**at which you want to calculate the sound level.**Plug the values into the decibel distance formula**:**L2 = L1 – 20 log10(d2/d1)****Solve the equation**to find the final sound level (**L2**).

When the initial sound level is **100 dB** at a distance of **1 meter**, and you want to find the sound level at **5 meters**, you would plug in the values as follows:

L2 = 100 – 20 log10(5/1)L2 = 100 – 20 × 0.699L2 = 100 – 13.98L2 = 86.02 dB

At a distance of **5 meters**, the sound level would be approximately **86 dB**.

A loudspeaker produces **110 dB** at **1 meter**. Calculate the sound level at **50 meters**:

L1 =

110 dB, r1 =1 meterr2 =

50 metersL2 = 110 – 20

log10(50 / 1)1.69897

= 110 – 20

= 110 –33.9794

=76.0206 dB

## How Far Do 100 Decibels Travel?

When initial sound level is **100 dB** at **1 meter**, it will drop to **60 dB** at a distance of approximately **100 meters**.

The distance that **100 decibels** can travel depends on several factors, such as the **environment**, **obstacles**, and **atmospheric conditions**. However, we can use the **decibel distance formula** to estimate the distance at which the sound level drops to a certain level.

Let’s say we have a sound source that produces **100 dB** at a distance of **1 meter**. We want to find the distance at which the sound level drops to **60 dB**. We can rearrange the formula to solve for **d2**:

L2 = L1 – 20 log10(d2/d1)60 = 100 – 20 log10(d2/1)20 log10(d2/1) = 40log10(d2/1) = 2d2/1 = 10^2 = 100d2 = 100 meters

## What is the 6 dB Rule for Distance?

The **6 dB rule** for distance is a simplified way to estimate the change in sound level when the distance from the source is doubled or halved. It states that:

**When the distance from the sound source is doubled**, the sound level**decreases**by approximately**6 dB**.**When the distance from the sound source is halved**, the sound level**increases**by approximately**6 dB**.

This rule is based on the **inverse square law** and the **logarithmic nature** of decibels. Since decibels increase exponentially, a **6 dB change** corresponds to a **fourfold change** in sound intensity.

For example, if a sound source has a level of **100 dB** at a distance of **1 meter**, and you move to a distance of **2 meters**, the sound level will drop by approximately **6 dB**, resulting in a level of **94 dB**. Conversely, if you move from **2 meters** to **1 meter**, the sound level will **increase** by **6 dB**, reaching **106 dB**.

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