Formula of Average Speed: Total Distance / Total Time

The formula of average speed is $v_{avg} = \frac{\text{total distance}}{\text{total time}}$ . Add up every metre the object travelled, add up every second the trip took, and divide the first total by the second. Stops, slow patches and fast stretches are all inside those two totals.

Average speed is a scalar, so it never has a direction and is never negative. It is the number a trip computer shows at the end of a drive. The idea is simple, but the averaging step catches students all the time, because the average of two speeds is usually not the average speed.

Quick facts

Formula
$v_{avg} = \frac{d_{total}}{t_{total}}$
SI unit
m/s (km/h for road trips)
Dimensional formula
[M⁰ L¹ T⁻¹]
Type
Scalar
Two equal distances
$\frac{2v_1 v_2}{v_1 + v_2}$
Two equal times
$\frac{v_1 + v_2}{2}$

Formula of average speed: what goes on top and bottom

The parts of the average speed formula
Part	What to include	SI unit
Total distance	The sum of every leg, each as a positive length	m
Total time	Every second from start to finish, including rests	s
Average speed	Their ratio	m/s

The most common slip is to leave out a rest stop. If a bus waits 10 minutes at a station, those 10 minutes are part of the trip time, and they pull the average speed down.

Trip problems solved step by step

Example 1: a road trip with a break

A family drives 120 km in 2.0 h, stops for 0.5 h, then drives 60 km in 1.5 h. Find the average speed.

Total distance = 120 + 60 = 180 km. Total time = 2.0 + 0.5 + 1.5 = 4.0 h.

$v_{avg} = \frac{180}{4.0} = 45\ \text{km/h}$

In SI units: 45 ÷ 3.6 = 12.5 m/s.

Example 2: a run then a walk

An athlete runs 400 m in 50 s, then walks 100 m in 50 s. Find the average speed.

$v_{avg} = \frac{400 + 100}{50 + 50} = \frac{500}{100} = 5.0\ \text{m/s}$

Example 3: up and down a hill

A hiker climbs a 6.0 km trail at 3.0 km/h and comes back down the same trail at 6.0 km/h. Find the average speed for the round trip.

Time up = 6.0 ÷ 3.0 = 2.0 h. Time down = 6.0 ÷ 6.0 = 1.0 h. Total distance = 12 km in 3.0 h.

$v_{avg} = \frac{12}{3.0} = 4.0\ \text{km/h}$

Not 4.5 km/h. The hiker spends twice as long going up, so the slow speed counts for more.

Equal distances and equal times

Example 3 shows a pattern worth learning. When an object covers two equal distances at speeds v₁ and v₂, the average speed is the harmonic mean:

$v_{avg} = \frac{2 v_1 v_2}{v_1 + v_2}$

Check it on the hiker: $\frac{2 \times 3 \times 6}{3 + 6} = \frac{36}{9} = 4$ km/h. When the object instead spends equal times at the two speeds, the simple mean is correct. Twenty minutes at 30 km/h and twenty minutes at 60 km/h give 45 km/h, because each speed lasts equally long.

If a question says equal distances, do not add the two speeds and halve them. Work out each time first.

Average speed and average velocity

The two use the same unit but different tops. Average speed divides the path length, while the average velocity formula divides the displacement. The hiker above finishes where she started, which leaves her with no net displacement and an average velocity of nothing, yet her average speed is 4.0 km/h. Average speed is always at least as big as the size of the average velocity.

For a single steady stretch, the plain formula of speed is enough. Average speed is what you need once a trip has parts.

Units and a quick sense check

Keep distances in one unit and times in one unit before dividing. For road trips, km and hours give km/h directly. For lab or sports problems, metres and seconds give m/s. A road speed in km/h becomes m/s once you take 3.6 out of it. The dimensions of average speed are length over time, [M⁰ L¹ T⁻¹], the same as any speed.

A sense check helps: the average speed of a trip must lie between its slowest and fastest stage speeds, and it is pulled toward the stage that lasted longest. For more rearrangements, see the speed distance and time triangle, or browse the kinematics formulas collection.

Frequently asked questions

What is the formula of average speed?

Average speed = total distance travelled / total time taken. Include stops in the total time.

Why is average speed not the average of the speeds?

Because the object spends different amounts of time at each speed. Halving the sum of two speeds is right only if each one lasted the same number of seconds.

What is the average speed for two equal distances?

Use 2v₁v₂ / (v₁ + v₂). A cyclist covering equal halves at 10 m/s and 15 m/s averages 12 m/s, not 12.5 m/s.

Can average speed be zero?

Only if the object does not move at all. Any motion adds distance, so average speed is positive even for a round trip.

How is average speed different from average velocity?

Average speed uses total distance and is a scalar. Average velocity uses displacement and is a vector, so it can be zero on a round trip.