The Verification Venue · light is instant, sound runs late
The Mile Sound Runs Late
You see the flash the instant it happens. Light crosses ten miles in about fifty microseconds, so the whole wait before the thunder is just sound crossing the air to you. Count the seconds, divide by five for miles. It is a good rule. It is also, quietly, a rounding, and the thing you would reach for to correct it is the wrong thing.
The rule everyone learns is real and it is honest: count the seconds from flash to bang, divide by 5 for miles (divide by 3 for kilometres). But five is a rounding of the 4.7 seconds a mile of air actually costs at 20 C, so the rule reads the storm about 6 percent closer than it is. Drive the bench below: tap the flash, tap the bang, then drag the temperature and watch the rounding error beat the temperature effect, every number recomputing in front of you.
Hearing safety: the clap is a soft synthesized rumble at low volume. Turn your device down first if you use headphones.
The rule (÷ 5)
2.00 mi
10 s ÷ 5
The physics (s × c)
2.13 mi
10 s × 343 m/s
The rule minus the physics
-6.2%
the rule reads short
Speed of sound c(T)
343 m/s
at 20 C
Temperature the "÷ 5" rule assumes
≈ -15.5 C
back-solved from c = 1609.344 / 5 = 321.9 m/s: a cold winter day
30-30 legacy chip
within 6 mi
NWS now says: when thunder roars, go indoors. Wait 30 min after the last clap.
Frozen interval
10.00 s
flash to bang
What this number is, and is not. Flash-to-bang gives the distance to the nearest point of a lightning channel that can be several kilometres long, not the ground strike-point or the storm's centre. And it tells you where the lightning is, not whether you are safe: NWS warns lightning can strike as far as 10 miles from where it is actually raining, a "bolt from the blue".
Sound moves faster in warm air. Watch how little the distance moves.
The km rule (2.9 rounded to 3) is the more faithful of the two.
The number for c changes; the physics does not.
Set a hidden distance, fire the demo, then tap along.
Speed of sound c(T), computed two independent ways
Near room temperature the two models agree to about a fifth of a metre per second, widening to under 1 m/s only out at 40 C.
Practice mode: fire a demo storm
Set a hidden true distance with the slider above, press Fire, watch for the flash, then tap at the flash and again at the bang. The demo knows the exact sound delay, so it can show you how much your own reaction time (about 0.2 to 0.4 s per tap) crept into the count. That latency is real, and it is the honest limit of the mental method.
Armed for a demo. Fire it, then tap along.
Rule audit: does the bench reproduce the NWS worked example?
NWS JetStream states it verbatim: see the flash, count 10 seconds to the thunder, and the lightning is 2 miles away (10 ÷ 5 = 2).
The knob that barely turns
Here is the reversal the thin explainers miss. The thing people reach for to fix the count is temperature, and it is a red herring. Across the whole realistic weather band, 0 to 30 C, the true seconds-per-mile moves only from 4.86 to 4.61, a swing of about a quarter of a second. Rounding 4.69 up to 5 is already a gap of about a third of a second, and it always leans the same way. The bracket below the curve is the rounding gap; the whole temperature slope of the curve is no bigger.
Seconds-per-mile falls gently from about 5.05 at -20 C to about 4.54 at +40 C. A dashed line marks the rule's divisor of 5. Across the everyday 0 to 30 C band the curve spans only 4.86 to 4.61 (about 0.25 s), which is smaller than the 0.31 s gap between the rule's 5 and the true 4.69 at 20 C. The rounding is the bigger error, and it always makes the rule read the storm slightly closer than it is.
What the number cannot tell you
The count locates the lightning. It does not clear you.
Two honesties the fifty thin calculators skip. First, geometry: the flash you see is a channel several kilometres long, and the first thunder you hear comes from the nearest point of that discharge. So flash-to-bang measures distance to the closest part of the strike, not to the ground contact point or the storm's core. Second, and this is the one that matters, the number answers "where", not "am I safe". NWS warns that lightning can strike as far as 10 miles from where it is raining, the "bolt from the blue", which is exactly why the official message dropped the reassuring 30-30 arithmetic for a flat "when thunder roars, go indoors". A page that turns flash-to-bang into a safety gauge is making the very error the rule's own authors walked back. Treat the 30-30 chip on the bench as a legacy heuristic, not today's rule.
And the audible range is a soft edge, not a wall. Thunder is normally audible only out to about 10 miles (16 km), because the air usually cools with height and refracts the sound waves upward away from the ground, on top of ordinary attenuation. A temperature inversion (warm air over cold) can bend the sound back down and stretch the range to 15 or 20 miles. So "no thunder" is not "no lightning".
The two rules, side by side
| Miles: divide by 5 | Kilometres: divide by 3 | |
|---|---|---|
| True seconds per unit at 20 C | 4.69 s / mi | 2.91 s / km |
| Rounded divisor the rule uses | 5 | 3 |
| Fraction of true distance returned | 93.8% | 97.1% |
| How far short it reads | about 6% short | about 3% short |
| Speed the divisor implies | 321.9 m/s (~ -15.5 C) | 333.3 m/s (~ +3 C) |
| Direction of the error | storm is farther than the count | storm is farther than the count |
The check: every number recomputed in front of you
Nothing here is stored. For your current settings the page recomputes the whole chain from the same constants the offline verifier uses, live:
The offline gate recomputes all of it, two independent ways where it can: node research/how-far-away-is-the-lightning/verify-how-far-away-is-the-lightning.mjs. Free choices & scope. The exact-physics distance uses the Newton-Laplace speed of sound c = 331.3·√(1 + T/273.15), which gives 343.2 m/s at 20 C; the linear 331.3 + 0.606·T is shown alongside and the two are used interchangeably because they agree to a fraction of a m/s near room temperature. The mile is the international mile, exactly 1609.344 m; the kilometre is 1000 m; the speed of light is 2.998×108 m/s. Humidity and altitude shift c by well under a percent near the ground and are not modelled; the effect is smaller than the rounding the page is about. Tap latency in practice mode is your real reaction time, not a model.
What is exactly true here, and what is a model or a choice
Exactly true. You see the flash essentially instantly: light crosses 10 miles in 5.37×10-5 s, less than one part in ten thousand of any thunder lag, so the whole delay is sound. Sound near the ground at 20 C moves at about 343 m/s, so a mile of air takes 1609.344 / 343.2 = 4.69 s and a kilometre takes 1000 / 343.2 = 2.91 s. "Divide by 5" therefore returns 4.69 / 5 = 93.8% of the true distance (about 6% short) and "divide by 3" returns 2.91 / 3 = 97.1% (about 3% short), both leaning the same way: the storm is a touch farther than the count says. The divisor 5 corresponds to sound at 1609.344 / 5 = 321.9 m/s, the speed at roughly -15.5 C, so the rule is effectively calibrated for a cold day.
The temperature claim, scoped. Over the everyday 0 to 30 C band the true seconds-per-mile runs 4.86 to 4.61, a swing of about 0.25 s that is smaller than the 5 - 4.69 = 0.31 s rounding gap baked into the rule. Push the slider into deep cold and the divisor 5 does become accurate (that is the -15.5 C readout), but across ordinary storm weather, temperature is the smaller correction, not the larger one.
A model or a choice. The exact-physics line uses Newton-Laplace c(T); the two speed-of-sound models are textbook standard and agree to about 0.2 m/s at 20 C, 0.3 m/s at 25 C, and 0.8 m/s by 40 C. The 30-30 chip is a legacy NWS heuristic shown with the current "when thunder roars, go indoors" message; it is not presented as today's official rule. The audible 10 mile / 16 km figure is the NORMAL range, extendable to 15 to 20 miles under inversions or terrain, not a hard cutoff. Humidity, altitude, wind and the finite length of the lightning channel all shift the real number a little; the page names them rather than pretending they are zero.