# Lightning Distance Calculator

Created by Davide Borchia
Last updated: Feb 18, 2023

Every time a thunderstorm rages, the light knows that it has to run faster than the sound to allow you to calculate the lightning distance. With a bit of physics and very little math, you can quickly discover your distance from a storm: learn how with us!

With our lightning distance calculator, we will guide you in a quick exploration of one of the most awesome and fear-inducing atmospheric phenomena.
Here you will learn:

• What is lightning;
• How to calculate the distance of a storm using the time between lightning and thunder;
• Examples of how to calculate the distance of lightning; and
• The proper distance from lightning and thunder: Omni safety tips!

## What is a lightning? An explanation in record time for lightning and thunder

The atmosphere is quite a lively place: from breezes to jet streams, from hail to ever-mutating clouds, there's surprisingly little place for a calm and relaxing blue sky. The lightning is probably the most famous, feared, and respected phenomenon in the sky: let's learn more about it!

Lightning is an electric discharge that happens naturally in the presence of a high potential difference between two points in the atmosphere or between the atmosphere and the ground.

Lightning originates from causes still unknown: what we know is that ionized channels open from both sides of the potential difference (the lightning's leaders), connecting two regions with a negative and positive charge. Once the channel is "completed", a strong current flows from cloud to ground. The energy of the current ionizes the air molecules, creating a plasma hotter than the surface of the Sun (way hotter: $50,000\ \text{K}$, ten times the surface of our star).

Plasma is the fourth state of matter, where a portion of — or all — the electrons are "ripped" away from an atom, leaving a highly charged substance with high conductivity. Plasma is the most common state of matter since stars are literally huge plasma balls!

The plasma is the key! Being so hot, it causes the gases surrounding it to expand explosively. The consequence is a loud bang, the thunder.

The color of lightning is usually white. However, there are small variations. One of the reasons is the plasma: each gas in a plasma state emits light at a specific frequency. Oxygen and nitrogen shine with a violet/lilac hue, easy to spot in lightning. The intense white color is due to the extreme heat (check our Wien's law calculator to learn more). Other hues are given by the scattering of this white light in the atmosphere.

## How far away is the lightning? How the time between thunder and lightning allows us to calculate the distance of a lightning

A lightning strike is instantaneous; however, at a distance, lightning and thunder arrive at different times. How so?

It's time for some physics: we deal with two entirely different phenomena: light and sound. Each of them propagates in a given medium at different speeds: the speed of light and the speed of sound.

The speed of light in Earth's atmosphere has value:

$c = 299,\!702,\!547\ \frac{\text{m}}{\text{s}}$

Or:

$c = 983,\!276,\!073\ \frac{\text{ft}}{\text{s}}$

Slightly less than the value of the speed of light in a vacuum. This speed is out of the charts: a flash on the Moon would reach Earth in just above a second. We can safely assume that the light of the lightning flash reaches you instantaneously.

Let's check the other player, sound. In our atmosphere, the sound moves at:

$v_\text{s} = 343\ \frac{\text{m}}{\text{s}}$

Or

$v_\text{s} = 1,\!125.3\ \frac{\text{ft}}{\text{s}}$

To tell how far lightning is, it's better to use the values of the speed of sound in miles and kilometers per second:

\begin{align*} v_\text{s}= 0.343\ \frac{\text{km}}{\text{s}} \\ v_\text{s} = 0.213\ \frac{\text{mi}}{\text{s}} \end{align*}

Now it's time to use the time between lightning and thunder to calculate the distance of lightning. The formula is akin to a speed formula: distance over speed:

$v_\text{s} = \frac{d_\text{l}}{t}$

Where:

• $t$ is the time, expressed in seconds, between lightning and thunder; and
• $d_\text{l}$ is the distance: how far away lightning is.

To calculate the distance, we only have to rearrange the formula for the distance keeping the speed of sound and the lightning to thunder time on the same side:

$d_\text{l} = v_\text{s}\cdot t$

Lightning strikes! Usually, it's not scary; after all, it's just light. Start counting the seconds: you have a few options. Starting from the most complicated:

• Measure time with a clock; or
• Count! The old trick still holds: one Mississippi, two Mississippi, three Mississippi....

Now you have all the data:
If you are chilling indoors, light up our lightning distance calculator, insert the time you found, and enjoy the storm in the safety of your place. Whenever the storm hits, we like to open the : isn't it cool that we can detect lightning (almost) worldwide, in real-time?
If a calculator is not available (maybe

• If you are counting in miles, divide the time by $5$;
• If you are counting in kilometers, divide the time by $3$.

It's that easy!

## Too close! Example of how to calculate the distance of a lightning

We are pretty sure that the best question to ask is "how far is lightning from me" and not "how close is lightning to me"!

If you see the flash, and you count up to 30 seconds between lightning and thunder, the bolt struck:

\begin{align*} d_\text{l} &= v_\text{s}\cdot t = 0.343\ \frac{\text{km}}{\text{s}}\cdot 30\ \text{s} \\ &= 10.29\ \text{km} \\ & = 0.213\ \frac{\text{mi}}{\text{s}}\cdot 30\ \text{s} \\ &= 6.39\ \text{mi} \\ \end{align*}

It looks like you're safe. What if you count only up to 5? We can approximate this time: use the rule of thumb, divide by $5$ the time, and run! The lightning struck a mile away!

#### Lighthning safety 101

One, two, three, fo- thunder! This time it struck a bit too close: you may not be safe. If you are inside, wait a bit: unless you are at the estuary of Rio Catatumbo, the storm will likely end soon. If you are outside, follow these rules to be a bit safer!

If the thunder hits before you count to $30$, you are probably too close to the storm: seek refuge!

• Avoid sheltering under isolated objects like trees. Those are lightning magnets.
• Stay away from metal and water.
• If you are in the mountain, don't cover under rock walls: they can conduct electricity better than air!
• Even though it feels counterintuitive, lay down and crouch. The smaller you are, the less likely you are a target for lightning.
• Power off your electronics, and keep antennas away. Bolts of Lightning like points!
• Get away from elevated points.
• Cars are safe: we are talking of Faraday's cages!
• Even though you can't see lightning, if you hear thunder, you are in danger!

Another thing: trust your feelings! Before lightning strikes, the electric potential builds up around the "target" area. If you are — unluckily — there, you would feel it. Your , your skin would tingle, and you would hear buzzing sounds. Do only one thing: !

Davide Borchia
Time between flash and thunder
s
Storm distance
mi
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