Ultrasonic Distance Measurement
d = v × t / 2
Quick answer
This calculator solves d = v_sound × t / 2, v_sound ≈ 343 m/s at 20°C for Distance. With Round-Trip Time 100 µs, the result is 1.715 cm. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Ultrasonic distance sensors measure the time for a sound pulse to travel to a target and return (echo). Since the sound travels to the target and back, the one-way distance is half the round-trip time multiplied by the speed of sound. The speed of sound in air at 20°C is approximately 343 m/s (0.0343 cm/µs). Temperature affects the speed of sound significantly: v ≈ 331.3 + 0.606 × T(°C) m/s. Common ultrasonic sensors like HC-SR04 measure distances from 2 cm to 400 cm with ±3 mm accuracy.
Variables
- d — Distance to target (m)
- t — Round-trip echo time (s)
Practical Notes
At 20°C, sound travels about 0.343 mm/µs or 34.3 cm/ms. A target at 1 m distance produces a round-trip time of 2/343 ≈ 5.83 ms. The minimum detectable distance is limited by the transmit pulse duration (typically 0.3-1 ms, corresponding to 5-17 cm minimum range). Maximum range is limited by signal attenuation and beam spreading. Temperature compensation improves accuracy: at 0°C, v = 331 m/s (−3.5%); at 40°C, v = 355 m/s (+3.5%).
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| d | Distance | cm | mm, cm, m, km |
| t | Round-Trip Time | µs | ps, ns, µs, ms, s, min, h |
Step by step
- 1. What you know: Round-Trip Time 100 µs
- 2. The relation: d = v_sound × t / 2, v_sound ≈ 343 m/s at 20°C
- 3. Substitute: t = 100 µs
- 4. Result: Distance = 1.715 cm
Worked examples
Minimum range
Given: Round-Trip Time 100 ns
Result: Distance = 0.01715 mm
Low range
Given: Round-Trip Time 1 µs
Result: Distance = 0.1715 mm
Typical
Given: Round-Trip Time 100 µs
Result: Distance = 1.715 cm
High range
Given: Round-Trip Time 0.5 ms
Result: Distance = 8.575 cm
Maximum range
Given: Round-Trip Time 5 ms
Result: Distance = 0.8575 m
Solving for each variable
Solve for Distance
Round-Trip Time 100 ns → 0.01715 mm
Solve for Round-Trip Time
Distance 1 mm → 5.831 µs
How Distance changes with Round-Trip Time
| Round-Trip Time (input) | Distance (result) |
|---|---|
| 10 µs | 1.715 mm |
| 25 µs | 4.288 mm |
| 50 µs | 8.575 mm |
| 75 µs | 12.86 mm |
| 100 µs | 1.715 cm |
| 150 µs | 2.573 cm |
| 0.2 ms | 3.43 cm |
| 0.4 ms | 6.86 cm |
| 0.7 ms | 12.01 cm |
| 1 ms | 17.15 cm |
The same result in other units
| Unit | Value |
|---|---|
| mm | 17.15 |
| cm | 1.715 |
| m | 0.01715 |
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<p><a href="https://vbatpower.com/formulas/ultrasonic-distance/">Ultrasonic Distance Measurement</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Ultrasonic Distance Measurement?
Use d = v_sound × t / 2, v_sound ≈ 343 m/s at 20°C. With Round-Trip Time 100 µs, Distance works out to 1.715 cm.
What is the formula for Ultrasonic Distance Measurement?
The formula is d = v_sound × t / 2, v_sound ≈ 343 m/s at 20°C. Ultrasonic distance sensors measure the time for a sound pulse to travel to a target and return (echo).
How do you find Round-Trip Time when you know the other values?
Rearrange for Round-Trip Time: with Distance 1 mm, Round-Trip Time is 5.831 µs.
What units does Ultrasonic Distance Measurement use?
Distance is shown in mm, cm, m. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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