Displacement Definition: What Is Displacement?
In physics (and geometry), displacement is the change in position of an object — the straight-line distance from the starting point to the ending point, regardless of the path taken to get there. It is a vector quantity, meaning it has both magnitude and direction.
Displacement is different from distance. Distance measures the total length of the path traveled, while displacement measures only how far — and in what direction — an object ended up from where it started. For example, if you walk 3 km north and then 3 km south, your total distance traveled is 6 km, but your displacement is 0 km (you're back at the start).
The SI unit of displacement is the meter (m). In the US customary system, displacement is typically measured in feet (ft).
How to Calculate Displacement: Displacement Formula
There are three common displacement formulas depending on what information you have:
Formula 1: From Average Velocity and Time
d = v × t
- d = displacement (m or ft)
- v = average velocity (m/s or ft/s)
- t = time (seconds)
This is the simplest formula. Use it when you know the average (constant) velocity and the time interval. For example: a car travels at 20 m/s for 5 seconds → displacement = 20 × 5 = 100 m.
Formula 2: From Initial Velocity, Acceleration, and Time
d = v₀t + ½at²
- d = displacement (m or ft)
- v₀ = initial velocity (m/s or ft/s)
- a = acceleration (m/s² or ft/s²)
- t = time (seconds)
Use this formula when an object starts with an initial velocity and accelerates (or decelerates) uniformly. It's one of the classic SUVAT equations of kinematics. For example: a ball is thrown upward at 15 m/s with gravitational deceleration of −9.81 m/s² for 2 seconds → d = 15(2) + ½(−9.81)(4) = 30 − 19.62 = 10.38 m.
Formula 3: From Initial and Final Velocity
d = (v₀ + v) / 2 × t
- d = displacement (m or ft)
- v₀ = initial velocity (m/s or ft/s)
- v = final velocity (m/s or ft/s)
- t = time (seconds)
Use this when you know both the starting and ending velocities and the time elapsed. The formula calculates the average velocity first, then multiplies by time. For example: a train accelerates from 0 m/s to 30 m/s over 60 seconds → d = (0 + 30) / 2 × 60 = 900 m.
How to Use the Displacement Calculator
- Choose a unit system — Metric (m, m/s, m/s²) or Imperial (ft, ft/s, ft/s²).
- Select a calculation mode:
- Velocity × Time: Enter average velocity and time.
- Acceleration: Enter initial velocity, acceleration, and time.
- Two Velocities: Enter initial velocity, final velocity, and time.
- Fill in the values and click Calculate.
- The calculator shows the displacement, the formula used with your values plugged in, and a full unit conversion table (m, km, cm, ft, in, yd, mi).
Displacement vs. Distance: Differences and Similarities
| Property | Displacement | Distance |
|---|---|---|
| Type | Vector (has direction) | Scalar (no direction) |
| Path dependence | Path-independent (straight-line) | Path-dependent (total length) |
| Can be zero? | Yes — if start = end point | Only if no movement |
| Can be negative? | Yes — depends on direction | Never negative |
| Formula | d = v × t (or SUVAT) | Total path length |
The key insight: displacement is the shortest path between two points (a straight line), while distance is the actual path walked. For round trips, displacement is zero even though distance is not.
Velocity vs. Speed
The displacement formula uses velocity, not speed. Velocity is a vector — it includes direction. Speed is the magnitude of velocity (always positive). When an object reverses direction, its velocity becomes negative, reducing the net displacement even if the object is still moving fast.
Unit Conversion Reference
| From | To meters (m) |
|---|---|
| 1 foot (ft) | 0.3048 m |
| 1 inch (in) | 0.0254 m |
| 1 yard (yd) | 0.9144 m |
| 1 mile (mi) | 1609.344 m |
| 1 kilometer (km) | 1000 m |
| 1 centimeter (cm) | 0.01 m |
FAQs
- What is displacement in physics?
- Displacement is the change in position of an object — the straight-line vector from its starting point to its ending point. It has both magnitude and direction.
- Is displacement the same as distance?
- No. Distance is the total path length traveled. Displacement is the straight-line distance between the start and end positions. They are equal only when the object moves in a straight line without reversing.
- Can displacement be negative?
- Yes. Displacement is negative when the final position is behind the starting position (relative to the chosen positive direction). For example, moving 5 m to the left when right is positive gives a displacement of −5 m.
- What is the SI unit of displacement?
- The SI unit of displacement is the meter (m). Other common units include feet (ft), kilometers (km), and miles (mi).
- What is the difference between displacement and velocity?
- Displacement (d) measures how far an object has moved from its starting point. Velocity (v) measures how fast and in what direction the object is moving. The relationship is d = v × t for constant velocity.
- How do I calculate displacement with acceleration?
- Use the formula d = v₀t + ½at², where v₀ is the initial velocity, a is the acceleration, and t is the time. This is one of the SUVAT kinematic equations.