Formula & Calculator
Time-of-Flight (LiDAR) Distance Measurement
Calculates the distance to an object from the round-trip travel time of a light pulse, as used in LiDAR and laser rangefinders.
Interpretation
d = (c × t) / 2. Distance from time‑of‑flight measurement using light speed c. Used in LiDAR and laser rangefinders.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| d | Distance to the object | m |
| c | Speed of light in vacuum (or air, approximately) | 3e8 m/s |
| t | Round-trip travel time of the light pulse | s |
What it means
Time‑of‑flight sensors measure the time it takes for a light pulse (laser) to travel to an object and back. The distance is calculated using the speed of light c. This is the principle behind LiDAR. Understanding this is fundamental for 3D mapping and autonomous vehicle sensing.
Worked example
LiDAR Distance Measurement – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| c (m/s) | 300000000 |
| t (s) | 1e-9 |
| Parameter | Value |
|---|---|
| c | 300000000 |
| t | 3.33e-9 |
Common mistakes
- LiDAR Time‑of‑Flight distance: d = (c × t) / 2 – where c is the speed of light.
- c: 3.00×10⁸ m/s – constant.
- t: Round‑trip time – in seconds.
- Units: d in metres.
- Accuracy: Affected by timing precision – often uses pulse or phase measurement.
Applications
Time‑of‑flight (LiDAR) distance measurement, d = (c × t)/2, calculates the distance to a target by measuring the round‑trip time of a laser pulse. This is the principle behind LiDAR sensors used in autonomous vehicles, drones, and surveying. Engineers use it to generate 3D point clouds, to perform terrain mapping, and to detect obstacles. By using the speed of light c, this method offers high accuracy and long range. This formula is essential for modern perception systems in robotics and autonomous navigation.
- 3D mapping and environmental sensing for autonomous vehicles
- Obstacle detection and collision avoidance
- Surveying and topographic mapping
- Forestry and agriculture (canopy height measurement)
- Augmented reality and depth sensing
Frequently Asked Questions
The distance to an object is d = (c · t) / 2, where c is the speed of light (≈3×10⁸ m/s) and t is the round‑trip time of a light pulse.
Forgetting to divide by 2, since the measured time is the round trip.
Millimeter‑level accuracy is common for high‑end LiDAR, while cheaper units may have centimeter accuracy.
LiDAR has faster update rates, longer range, and better angular resolution. Ultrasonic is cheaper and works on transparent objects, but is slower and less accurate.
From a few meters (indoor robots) to hundreds of meters (autonomous vehicles).
Ambient light, object reflectivity, and atmospheric conditions (fog, rain).
By using a rotating mirror or multiple lasers to scan the environment, measuring the angle of the emitted beam at the time of detection.
Autonomous vehicles, robotics, surveying, archaeology, and atmospheric studies.
Strong sunlight can saturate the detector, reducing range or accuracy. Some LiDARs use narrow‑band filters to mitigate this.
Measure the time between emission and detection of the pulse, then apply d = c·t/2.