What is the speed of sound formula in air?

The speed of sound in dry air is approximately v = 331.3 + 0.606 × T, where T is temperature in °C. At 20°C, the speed is about 343 m/s (767 mph). More precisely, v = 331.3 × √(1 + T/273.15) gives slightly more accurate values for extreme temperatures.

How fast does sound travel in different materials?

Sound travels faster in denser/stiffer media (counterintuitively — it's about stiffness, not density alone). Air ~343 m/s, water ~1,480 m/s, wood ~3,850 m/s, steel ~5,960 m/s, diamond ~12,000 m/s. Sound cannot travel through a vacuum (no molecules to transmit it).

Why is sound faster in water than air?

Water is denser AND much stiffer than air. v = √(K/ρ) where K = bulk modulus, ρ = density. Water has K ≈ 2.2 GPa vs air ~0.14 MPa — 16,000× stiffer. Density is 1000× higher. Net result: water sound speed is √(16,000/1,000) ≈ 4× higher.

How do I estimate distance using thunder?

Count seconds between flash and thunder, then divide. 5 seconds ≈ 1 mile (1.6 km). 3 seconds ≈ 1 km (0.6 mi). Lightning is instantaneous; sound takes ~3 s/km to reach you. Below 30 seconds total = storm within 10 km. Below 5 seconds = unsafe; seek shelter.

Mach 1 = the local speed of sound. Mach number M = object speed / sound speed. At sea level, 20°C: Mach 1 ≈ 343 m/s ≈ 1,235 km/h ≈ 767 mph. At 11 km altitude (much colder), Mach 1 ≈ 295 m/s ≈ 1,062 km/h. Mach number is normalized to local conditions.

Why does helium make my voice sound higher?

Helium is much less dense than air, so sound travels faster (~1,007 m/s vs 343 m/s). The resonant frequencies of your vocal tract scale with sound speed — higher v means higher resonances. Your vocal cords vibrate at the same frequency, but the harmonic content shifts up. Sulfur hexafluoride does the opposite (very dense, low pitch).

Does the speed of sound depend on frequency?

In normal media (air, water, most solids): essentially no — all frequencies travel at the same speed. This is why music sounds the same close up or far away (mostly). At extreme frequencies (GHz) or in certain solids, dispersion (frequency-dependent speed) can occur, but it's small for normal acoustic situations.

How is the speed of sound used in modern technology?

Sonar (underwater navigation, fish-finding), seismology (mapping Earth's interior), ultrasonic NDT (testing metal welds), medical imaging (ultrasound), echo localization (parking sensors), acoustic levitation (lab tools), audio engineering (room design, speaker placement), and aircraft engineering (Mach number for jets).

Speed of Sound Calculator

Calculate the speed of sound in air based on temperature. Uses the approximation v = 331.3 + 0.606 × T (°C) for dry air. Also shows the speed of sound in common materials like water, steel, and glass.

Last updated: May 30, 2026

About this calculator

The speed of sound describes how fast acoustic waves travel through a medium. Unlike electromagnetic waves (which need no medium), sound is a mechanical compression wave — molecules bumping into each other and passing energy along. The speed depends on the medium's properties: stiffer and lighter media transmit sound faster.

In dry air at room temperature (20°C), sound travels at ~343 m/s (767 mph). This is famously slow compared to light, which is why you see lightning before hearing thunder. The 5-second rule: every 5 seconds between flash and thunder ≈ 1 mile distance (or every 3 seconds ≈ 1 km).

Air temperature strongly affects sound speed because warmer molecules move faster, transmitting pressure pulses more rapidly. A simple linear approximation: v = 331.3 + 0.606 × T(°C). Humidity has a small additional effect (sound travels ~0.4% faster in 100% humid air vs dry at the same temperature). Pressure has almost no effect at typical atmospheric conditions.

Sound in water (~1,500 m/s) is ~4.4× faster than in air. In steel (~5,960 m/s), it's ~17× faster. In diamond (~12,000 m/s), ~35× faster. This is why you can hear an approaching train by putting your ear to the rail long before you'd hear it through air.

The Mach number is the ratio of object speed to local sound speed. M = 1 at the speed of sound. Aircraft exceeding Mach 1 produce sonic booms — the compression of air waves into shock fronts.

Common applications: aircraft design, sonar systems (underwater), seismology (sound in rock layers), audio engineering (microphone placement, room acoustics), atmospheric science, ultrasonic technology, and any acoustic analysis.

Formula

**Speed of sound in dry air (linear approximation):** v ≈ 331.3 + 0.606 × T Where T is temperature in °C, v in m/s. **More accurate formula (ideal gas):** v = 331.3 × √(1 + T/273.15) Or: v = √(γ × R × T / M) Where: - γ = ratio of specific heats (1.4 for air) - R = 8.314 J/(mol·K) - T = absolute temperature (K) - M = molar mass (0.02897 kg/mol for air) **Worked example: sound speed at 20°C** Linear: v = 331.3 + 0.606 × 20 = 331.3 + 12.12 = 343.4 m/s. Exact: v = 331.3 × √(1.0732) = 331.3 × 1.0360 = 343.2 m/s. Both agree well at moderate temperatures. **Temperature effect (air):** | Temperature (°C) | v (m/s) | v (mph) | |---|---|---| | -40 | 306.5 | 686 | | -20 | 319.1 | 714 | | 0 | 331.3 | 741 | | 10 | 337.4 | 755 | | 20 | 343.4 | 768 | | 25 | 346.4 | 775 | | 30 | 349.5 | 782 | | 40 | 355.5 | 795 | | 100 | 387.0 | 866 | About +0.6 m/s per °C. **Speed in different media:** | Medium | v (m/s) | Notes | |---|---|---| | CO₂ | 259 | heavier than air | | Air | 343 | at 20°C | | Helium | 1,007 | lighter than air (why "voice high"?) | | Hydrogen | 1,310 | lightest gas | | Water (fresh, 20°C) | 1,481 | | | Water (sea, 25°C) | 1,533 | more dense | | Rubber | 60-1,500 | depends on density | | Wood (typical) | 3,800-4,800 | along grain | | Concrete | 3,600-5,000 | | | Brass | 3,500 | | | Aluminum | 6,420 | high | | Iron | 5,950 | | | Steel | 5,960 | | | Granite | ~6,000 | | | Glass | 5,500-6,000 | | | Diamond | 12,000 | very stiff | | Beryllium | 12,890 | metal with highest v | **Why sound is faster in stiffer media:** v = √(K/ρ) for fluids, where K = bulk modulus, ρ = density. v = √(E/ρ) for solids, where E = Young's modulus. Higher stiffness → faster sound. Higher density → slower. Steel: high stiffness, moderate density → very fast. Lead: moderate stiffness, very high density → moderate (1,200 m/s). **Mach number:** M = v_object / v_sound | M | Regime | Examples | |---|---|---| | < 0.8 | Subsonic | most commercial aircraft, cars | | 0.8-1.0 | Transonic | airliners just below sound speed | | 1.0 | Sonic | sound speed exactly | | 1.0-5.0 | Supersonic | Concorde, fighter jets | | ≥ 5.0 | Hypersonic | reentry vehicles, missiles | Mach 1 at sea level (20°C): 343 m/s ≈ 1,235 km/h ≈ 767 mph. **Sonic boom physics:** When v_object > v_sound, pressure waves pile up into shock wave. Conical shock front trails the object. Mach cone angle: sin θ = 1/M. M = 2: cone angle ~30°. M = 5: cone angle ~11.5°. Listener hears sudden boom as shock passes, even if aircraft has already left. **Worked example: thunder distance** Lightning to thunder delay: 5 seconds. Distance? Speed of sound: 343 m/s. Distance = 343 × 5 = 1,715 m ≈ 1 mile. The "5-second rule" for thunder: count seconds, divide by 5 for miles (or 3 for km). **Sound in atmosphere:** | Altitude | Temperature | Speed of sound | |---|---|---| | Sea level | 15°C | 340 m/s | | 1 km | 8.5°C | 336 m/s | | 5 km | -17.5°C | 320 m/s | | 11 km (tropopause) | -56.5°C | 295 m/s | | 20 km | -56.5°C | 295 m/s | | 50 km | -2.5°C | 329 m/s | Speed depends only on temperature (in dry air), so it can increase or decrease with altitude depending on atmospheric layer. **Humidity effect:** Water vapor is lighter than dry air (M = 18 vs 29). Humid air has lower effective density → slightly faster sound. | Humidity | Speed change at 25°C | |---|---| | 0% | reference | | 50% | +0.15% | | 100% | +0.30% | Tiny effect compared to temperature. **Pressure effect:** For an ideal gas at constant T, v is independent of pressure. Real gases have small departures (~0.1% at extreme pressures), but for normal atmospheric variations, ignore. **Wavelength-frequency:** c = f × λ for sound: Audible (20 Hz - 20 kHz) wavelengths in air: - 20 Hz: 17.2 m. - 100 Hz: 3.43 m. - 1 kHz: 34.3 cm. - 10 kHz: 3.43 cm. - 20 kHz: 1.72 cm. Wavelength matters for: - Speaker design (subwoofers must be large; tweeters small). - Microphone placement (interference at half-wavelength). - Room acoustics (standing waves). - Ultrasonic imaging (high f → small λ → fine detail). **Underwater sound:** Sound travels 4× faster in water than air. Used for: - **Sonar**: detection by echo. - **Whale communication**: across ocean basins. - **Submarines**: stealth and detection. - **Marine biology**: tracking species. Underwater speed varies with temperature, salinity, depth (pressure). **Sound in solids (seismology):** Earth's interior characterized by sound wave speeds: - P-waves (compression): 5-13 km/s (fastest). - S-waves (shear): 3-7 km/s. Used to map Earth's structure (mantle, core boundaries). **Helium voice effect:** Helium has lower density than air → sound travels faster → resonance frequency of vocal tract is higher → high-pitched voice. Doesn't actually change vocal cord frequency, just the resonant filtering. Sulfur hexafluoride (SF₆): opposite effect — very dense gas → low pitch.

How to use this calculator

Enter air temperature in °C.
Calculator returns speed of sound in m/s, km/h, mph.
For other gases or materials, use specific values from tables.
For Mach number: divide object speed by sound speed at that altitude/conditions.
For sound distance: distance = speed × time. Thunder/lightning: 5 s ≈ 1 mile, 3 s ≈ 1 km.
Humidity changes are small (~0.3% max); temperature dominates.

Worked examples

Concert hall acoustics

**Scenario:** Symphony hall at 20°C. Concert pitch A (440 Hz) wavelength? **Calculation:** v = 343 m/s. λ = v/f = 343/440 ≈ 0.78 m (78 cm). **Result:** A4 wavelength is 78 cm. Sub-bass frequencies (40 Hz) have wavelength ~8.5 m — comparable to hall dimensions, creating standing wave resonances. Architects design halls to minimize problematic standing waves and balance frequency response.

Mach 2 fighter at altitude

**Scenario:** Fighter jet at Mach 2 at 11 km altitude (T = -56.5°C). Actual speed? **Calculation:** v_sound = 331.3 × √(1 + (-56.5)/273.15) = 331.3 × √(0.7931) = 331.3 × 0.8906 ≈ 295.0 m/s. v_jet = 2 × 295 = 590 m/s ≈ 2,124 km/h. **Result:** ~2,124 km/h (1,320 mph). At sea level, Mach 2 would be 686 m/s (2,470 km/h) — fighter at altitude moves slower in absolute terms but same Mach number. Mach is normalized to local conditions, which is more physically meaningful for aerodynamics.

Estimating storm distance

**Scenario:** Lightning seen, thunder heard 8 seconds later. **Calculation:** Distance = 343 × 8 = 2,744 m ≈ 1.7 miles ≈ 2.7 km. **Result:** Storm ~1.7 miles (2.7 km) away. Quick rule: divide seconds by 5 (miles) or 3 (km). At 8 seconds: 1.6 miles or 2.7 km. If thunder count decreases, storm approaching; if increases, departing. Below 5 seconds = within 1 mile = unsafe; seek shelter.

When to use this calculator

**Use speed of sound for:**

- **Acoustics**: room design, speaker placement, microphone setup. - **Aviation**: Mach number, sonic boom analysis. - **Sonar**: ranging in air or water. - **Meteorology**: thunder timing, atmospheric profiling. - **Underwater acoustics**: communication, navigation. - **Seismology**: Earth's interior from wave travel times. - **Industrial NDT**: ultrasonic flaw detection in metals. - **Medical ultrasound**: imaging through soft tissue (~1,540 m/s).

**Speed of sound key dependencies:**

- **Temperature**: dominant in gases. v ≈ 331 + 0.6T (°C). - **Medium type**: gas, liquid, solid all very different. - **Humidity** (air): small effect (+0.3% max). - **Pressure**: negligible for ideal gases. - **Direction**: usually isotropic in gases/liquids, anisotropic in some solids.

**Mach number in aviation:**

- **Mach < 0.3**: incompressible flow (most subsonic flight). - **Mach 0.3-0.8**: subsonic, compressibility starts mattering. - **Mach 0.8-1.2**: transonic — most complex aerodynamics. - **Mach 1-3**: supersonic. - **Mach > 5**: hypersonic, shock waves dominant.

Commercial jets: Mach 0.78-0.85 (sweet spot for fuel efficiency). Concorde (retired): Mach 2.04. SR-71 Blackbird: Mach 3.3+. Hypersonic experimental (X-15, X-43): Mach 5-10.

**Why we hear thunder later:**

Light reaches eye essentially instantly (300,000 km/s, indistinguishable from immediate). Sound: ~343 m/s — measurable delay.

1 km away: 2.9 second delay. 5 km away: ~15 second delay. 10 km away: ~30 second delay.

Beyond ~25 km, sound usually absorbed by atmosphere before arriving.

**Common applications:**

- **Audio equipment design**: room modes, speaker positioning. - **Cinema sound**: surround speakers optimized for delay/level. - **Stadium/auditorium acoustics**: avoiding echo and dead spots. - **Aircraft engines**: blade tip speed kept below local sound speed for efficiency. - **Race cars (LMP, F1)**: airbox optimization for sound transmission. - **Ultrasonic cleaning**: ~40 kHz typical frequency. - **Medical ultrasound**: 2-15 MHz for tissue imaging. - **Industrial sonar**: 30-300 kHz fish finders to oil prospecting.

**Anechoic chambers:**

Free from sound reflections. Used for: - Microphone calibration. - Speaker testing. - Aircraft noise measurement. - Sound-source localization research.

Quietest place on Earth: Microsoft anechoic chamber at -20.3 dBA.

**Wavelength and structure size:**

For sound to interact strongly with object, λ ≈ size.

| Frequency | Wavelength | Comparable size | |---|---|---| | 20 Hz | 17 m | building | | 200 Hz | 1.7 m | adult human | | 2 kHz | 17 cm | hand | | 20 kHz | 1.7 cm | finger |

This determines why subwoofers (low f) are insensitive to position and tweeters (high f) very directional.

**Underwater communication:**

Sound is the only practical signal underwater (radio absorbed quickly). - Whales: very low f (10-1,000 Hz) travels thousands of km. - Dolphins: 20-150 kHz for echolocation, ~5 km range. - SOFAR channel: low-loss sound duct at ~1,000 m depth. - Submarine sonar: 1-50 kHz active, broader passive listening.

**Software:**

- **MATLAB Acoustic Toolbox**: wave propagation. - **COMSOL Acoustic Module**: complex simulation. - **EASE / Odeon**: architectural acoustics. - **Underwater sonar**: NOAA, US Navy software.

**Pitfalls:**

- **Using sea-level sound speed at altitude**: temperature drops with altitude. - **Forgetting medium**: same frequency in water has different λ than in air. - **Helium voice misconception**: voice frequency doesn't change, just resonance. - **Mixing units**: m/s vs ft/s vs mph vs Mach. - **Sonic boom**: not just at moment of breaking sound barrier — continuously trails supersonic aircraft. - **Sound in solids**: longitudinal vs shear wave speeds differ. - **Pressure correction**: usually unnecessary for air but matters in deep water/high-altitude.

Common mistakes to avoid

Using "343 m/s" for all conditions (varies significantly with temperature).
Forgetting Mach number depends on local conditions (altitude).
Confusing speed of sound in air with other media (water 4× faster, steel 17×).
Thinking helium makes vocal cords vibrate faster (it changes resonance, not vocal cord frequency).
Using sea-level sound speed for high-altitude calculations.
Ignoring humidity in precision audio work.
Confusing speed of sound with intensity falloff (different physics).
Mixing units (m/s, ft/s, mph, knots, Mach).

Frequently Asked Questions

Sources & further reading

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Speed of Sound Calculator

Inputs

Temperature (°C)

Results

Speed in Air

343.2 m/s

Speed (km/h)

1235.6 km/h

Speed (mph)

767.8 mph

Speed of Sound Results

Parameter	Value
Temperature	20°C (68.0°F, 293.15 K)
Speed in Air	343.21 m/s
Speed in Air	1235.6 km/h (767.8 mph)
Mach 1 at this temp	343.21 m/s
Speed in Water (20°C)	1,481 m/s
Speed in Steel	5,960 m/s
Speed in Glass	4,540 m/s
Speed in Wood (oak)	3,850 m/s
Speed in Aluminum	6,420 m/s
Formula	v = 331.3√(T_K / 273.15)

Last updated: May 30, 2026

About this calculator

The Mach number is the ratio of object speed to local sound speed. M = 1 at the speed of sound. Aircraft exceeding Mach 1 produce sonic booms — the compression of air waves into shock fronts.

Formula

How to use this calculator

Enter air temperature in °C.
Calculator returns speed of sound in m/s, km/h, mph.
For other gases or materials, use specific values from tables.
For Mach number: divide object speed by sound speed at that altitude/conditions.
For sound distance: distance = speed × time. Thunder/lightning: 5 s ≈ 1 mile, 3 s ≈ 1 km.
Humidity changes are small (~0.3% max); temperature dominates.

Worked examples

Concert hall acoustics

Mach 2 fighter at altitude

Estimating storm distance

When to use this calculator

**Use speed of sound for:**

**Speed of sound key dependencies:**

**Mach number in aviation:**

Commercial jets: Mach 0.78-0.85 (sweet spot for fuel efficiency). Concorde (retired): Mach 2.04. SR-71 Blackbird: Mach 3.3+. Hypersonic experimental (X-15, X-43): Mach 5-10.

**Why we hear thunder later:**

Light reaches eye essentially instantly (300,000 km/s, indistinguishable from immediate). Sound: ~343 m/s — measurable delay.

1 km away: 2.9 second delay. 5 km away: ~15 second delay. 10 km away: ~30 second delay.

Beyond ~25 km, sound usually absorbed by atmosphere before arriving.

**Common applications:**

**Anechoic chambers:**

Free from sound reflections. Used for: - Microphone calibration. - Speaker testing. - Aircraft noise measurement. - Sound-source localization research.

Quietest place on Earth: Microsoft anechoic chamber at -20.3 dBA.

**Wavelength and structure size:**

For sound to interact strongly with object, λ ≈ size.

| Frequency | Wavelength | Comparable size | |---|---|---| | 20 Hz | 17 m | building | | 200 Hz | 1.7 m | adult human | | 2 kHz | 17 cm | hand | | 20 kHz | 1.7 cm | finger |

This determines why subwoofers (low f) are insensitive to position and tweeters (high f) very directional.

**Underwater communication:**

**Software:**

- **MATLAB Acoustic Toolbox**: wave propagation. - **COMSOL Acoustic Module**: complex simulation. - **EASE / Odeon**: architectural acoustics. - **Underwater sonar**: NOAA, US Navy software.

**Pitfalls:**

Common mistakes to avoid

Using "343 m/s" for all conditions (varies significantly with temperature).
Forgetting Mach number depends on local conditions (altitude).
Confusing speed of sound in air with other media (water 4× faster, steel 17×).
Thinking helium makes vocal cords vibrate faster (it changes resonance, not vocal cord frequency).
Using sea-level sound speed for high-altitude calculations.
Ignoring humidity in precision audio work.
Confusing speed of sound with intensity falloff (different physics).
Mixing units (m/s, ft/s, mph, knots, Mach).

About this calculator

Formula

How to use this calculator

Worked examples

Concert hall acoustics

Mach 2 fighter at altitude

Estimating storm distance

When to use this calculator

Common mistakes to avoid

Frequently Asked Questions

What is the speed of sound formula in air?

How fast does sound travel in different materials?

Why is sound faster in water than air?

How do I estimate distance using thunder?

What is Mach 1?

Why does helium make my voice sound higher?

Does the speed of sound depend on frequency?

How is the speed of sound used in modern technology?

Sources & further reading

Related Calculators

Doppler Effect Calculator

Frequency Calculator

Wavelength Calculator

Hooke's Law Calculator

Voltage Drop Calculator

Friction Force Calculator

Inputs

Results

Speed of Sound Results

About this calculator

Formula

How to use this calculator

Worked examples

Concert hall acoustics

Mach 2 fighter at altitude

Estimating storm distance

When to use this calculator

Common mistakes to avoid

Frequently Asked Questions

What is the speed of sound formula in air?

How fast does sound travel in different materials?

Why is sound faster in water than air?

How do I estimate distance using thunder?

What is Mach 1?

Why does helium make my voice sound higher?

Does the speed of sound depend on frequency?

How is the speed of sound used in modern technology?

Sources & further reading

Related Calculators

Doppler Effect Calculator

Frequency Calculator

Wavelength Calculator

Hooke's Law Calculator

Voltage Drop Calculator

Friction Force Calculator

Inputs

Results

Speed of Sound Results