Speed of Sound Calculator

Created by Hanna Pamuła, PhD candidate
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Sep 12, 2022

This speed of sound calculator determines the speed of sound in the air and water.

Not everybody knows about the sound speed dependence on the temperature – the higher the air temperature, the faster the sound can propagate.

To calculate the speed of sound in water, just choose the temperature – Fahrenheit °F or Celsius °C. You can also choose the desired unit – with this tool, you can find the speed of sound in mph, ft/s, or even knots!

Speed of sound in air

Air is almost an ideal gas. The formula for the speed of sound in ideal gases is:

$c = \sqrt{\frac{\gamma R T}{M}},$

where:

• $c$ – Speed of sound in an ideal gas;
• $R$ – Molar gas constant, approximately 8.314,5 J·mol−1·K−1;
• $γ$ – the adiabatic index, approximately 1.4 for air;
• $T$ – the absolute temperature; and
• $M$ – the molar mass of the gas. For dry air is about 0.028,964,5 kg/mol

Substituting the values for air, we have the simplified formula for the speed of sound in m/s:

$c_{\text{air}} = 331.3 \times \sqrt{\frac{1 + T}{273.15}},$

where $T$ is in °C.

Did you notice something interesting? The speed of sound in the gas depends only on two constants – $\gamma$ and $R$ – and on the temperature but not on the air pressure or density, as it is sometimes claimed. The humidity of air also has an effect on the speed of sound, but the influence is so small that it can be neglected. The temperature is the only important factor!

Speed of sound in water

The most often used value is 1482 m/s (for 20 °C); however, an easy formula for the speed of sound in water doesn't exist. Many authors derived equations from experimental data, but the equations are complicated, and they always contain higher-order polynomials and plenty of coefficients.

The data in our calculator for speed in water comes from the . The speed of sound in water is an important parameter in sonar research and acoustical oceanography. Nevertheless, the formula for seawater is even more complex as the speed of sound is also changing with the salinity.

How to use the speed of sound calculator?

Let's calculate how the sound propagates in cold water – like really cold, from wintering swimming activities.

1. Choose the section you need – the speed of sound in water or air. It's water in our case, so we will use the bottom part of the calculator.

2. Pick the temperature unit. Let's take degrees Fahrenheit.

3. Select the temperature from a drop-down list. Take this freezingly cold 40 °F.

4. The speed of sound calculator displays the speed of sound in water; it's 4672 ft/s.

5. Let's compare it with 90 °F (warm bath temperature). The speed is equal to 4960 ft/s this time. Remember that you can always change the units of speed of sound: mph, ft/s, m/s, km/h, even to knots if you wish to.

Now, as you know the speed, calculate the time or distance with this speed calculator. Also, you can check how far the storm is with our lightning distance calculator – the speed of sound in air is a significant factor for that calculations.

FAQ

How do I calculate the speed of sound in air given temperature?

To determine the speed of sound in air, follow these steps:

1. If you're given the air temperature in °C or °F, you need to first convert it to kelvins.
2. Add 1 to the temperature in kelvins and take the square root.
3. Multiply the result from Step 2 by 331.3.
4. You've just determined the speed of sound in the air in m/s – congrats!

How does the speed of sound change with temperature?

The speed of sound increases as the air temperature increases. The precise formula is:

c_air = 331.3 × √(1 + T/273.15),

where T is the air temperature in °C. This formula returns speed in m/s.

What is the speed of sound in air?

Assuming the air temperature of 20 °C, the speed of sound is:

• 343.14 m/s;
• 1235.3 km/h;
• 1125.8 ft/s; or
• 767.6 mph.

You can derive these results by applying the formula c_air = 331.3 × √(1 + T/273.15), where T = 20°C. The result is in m/s, and then, if needed, you have to convert it to other speed units.

What is the speed of sound in water?

Assuming the water temperature of 20 °C, the speed of sound is:

• 1481 m/s;
• 5332 km/h;
• 4859 ft/s; or
• 3313 mph.
Hanna Pamuła, PhD candidate
Speed of sound in dry air
Temperature
°F
Speed
ft/s
Speed of sound in water
I want to choose temperature in ...
°F
Temperature
70 °F
Speed
ft/s
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