Difference Between Distance & Displacement

Displacement is measured with a straight line between two points.

Distance is measured to determine how long a path between two points is. The odometer in your car measures distance as you travel from one location to another. Displacement, however, measures the straight-line distance between your starting point and your ending point. Distance is always equal to or greater than displacement.

Driving

Distance is always equal than or greater than displacement.

If you measure the distance between your starting location and your destination on a map, you can determine how many miles apart the two points are very accurately. Yet if you drive between those two points, your odometer will inevitably indicate that you traveled a greater distance. This is because you are probably not able to drive along a straight line between the two points. This distance you traveled should be accurately reflected by the odometer reading, while the displacement is accurately measured in a straight line on a map.

Floating in a River

Floating does not change your displacement relative to the water.

Consider rowing a boat in a river. If you do not use your oars, you will float downstream at the same velocity as the river. If you multiply the river's velocity by the amount of time you are drifting, you will get the distance you have traveled relative to the land. However, since you were not rowing, you have not moved any distance relative to the water.

Rowing Upstream

Rowing upstream does not change your displacement relative to the land.

Now consider the distance you travel, not relative to the land but relative to the water. As you start rowing upstream, you drop a small float in the river. If you row just fast enough to stay stationary relative to the land, your distance traveled and displacement relative to the land will be zero. However, if you measure how far away the float is after a certain amount of time, you can determine your change in distance relative to the water. Displacement would be measured in a straight line from your position relative to the position of the float.

Traveling Around the Globe

Special considerations on a sphere

If you fly exactly halfway around Earth, you will travel a distance of about 12,400 miles. But this is not a linear distance, it is a distance traveled around the sphere of the Earth. Your displacement is measured in a straight line from where you started--through the center of the Earth and not along its surface. This gives you a displacement equal to the diameter of the Earth, about 7,900 miles.

Vectors and Scalars

For purposes of mathematics and physics, distance is a simple measurement with regard to distance and does not have any regard for the direction taken while traveling. A value that has a magnitude without a direction (like distance) is known as a scalar. Displacement is a vector--it has a magnitude and direction. There are different rules for mathematics regarding scalars and vectors.

References

• NASA: Earth
• Texas State University: Linear Motion
• Electronic Science Tutor: Introduction to Vectors