Averaging speeds is not averaging numbers. It is total distance divided by total time, and the difference between 48 mph and 50 mph for the same two speeds is entirely a question of what was equal: the distances, or the times.

The one rule: total distance over total time

Average speed has exactly one definition: total distance divided by total time. Everything else in this guide is a consequence of that definition, and every mistake in averaging speeds comes from forgetting it. A speed is not a number you own; it is a ratio, distance over time, and ratios can only be averaged through the totals that made them. Add the distances, add the times, and divide once. Any method that skips the totals — adding the speeds and dividing by how many there are — answers a different question from the one you asked, and the answer it gives is wrong by an amount that grows with the difference between the speeds.

The reason is weighting. A speed held for longer weighs more in the average, because it covers more of the trip’s time. Drive fast for ten minutes and slow for two hours, and the slow speed dominates the average, however impressive the fast stretch felt. The plain average of the two speeds weights them equally, as if each had held for the same time, which is true only when the times really were equal. Mathematicians have a name for the equal-distance case: the harmonic mean. You do not need the name to use the rule, but it helps to recognise it when you meet it — whenever someone averages rates that were held over equal distances, equal amounts, or equal outputs, the harmonic mean is the honest average, and the plain mean is the trap.

Keep the units honest throughout. Speeds in miles per hour average only with speeds in miles per hour, and speeds in kilometres per hour only with their own kind. Convert first, then average, never the other way round — averaging 60 mph with 100 km/h as if they were the same unit gives a number that belongs to no system at all. The calculator on the Average Calculator page takes the same care: it averages the numbers you enter, and it is your job to make sure they are numbers of the same kind, over the same kind of base, before you trust the result.

Equal distances: the 60 and 40 case

The classic case is the round trip at two speeds. Drive 60 miles out at 60 mph and 60 miles back at 40 mph. The plain average of the two speeds is 50 mph, and it is wrong. The out leg takes exactly 1 hour. The return leg takes 1.5 hours, because 60 miles at 40 mph needs an hour and a half. The whole trip is 120 miles in 2.5 hours, and 120 divided by 2.5 is 48 mph. The slower leg took half as long again as the fast leg, so it pulls the average down toward itself — and the correct average, 48, sits closer to 40 than to 60, exactly as the times demand.

The general shortcut for two equal distances is worth memorising, because it skips the table: twice the product of the two speeds divided by their sum. Twice 60 times 40 is 4,800, divided by 100 is 48. It is the harmonic mean in disguise, and it works for any pair of equal distances — two laps, two halves of a journey, two equal stretches of road. It does not work when the distances differ, and it does not work when the times differ; for those, go back to the totals, which never fail. The error from the plain average is not academic: at 50 mph you would predict the 120-mile trip in 2 hours 24 minutes, six minutes sooner than the 2 hours 30 minutes it actually takes, and six minutes is the difference between arriving on time and explaining why you did not.

Notice what the equal-distance case teaches about intuition. Our instinct says the average of two speeds should sit halfway between them, and halfway between 60 and 40 is 50. But the average speed is not halfway in speed; it is weighted by time, and time is not split evenly between the legs. The slower you go, the longer each mile takes, so slow miles always count for more time than fast miles. Any average that ignores that asymmetry — the plain mean, a guess, a dashboard estimate — will overstate the speed whenever the slow stretch is long, which is precisely when overstating it costs the most.

Equal times: where the plain average does work

Change the setup and the plain average becomes correct. Drive 1 hour at 60 mph and 1 hour at 40 mph. Now the distances are 60 miles and 40 miles, the total is 100 miles in 2 hours, and the average is 50 mph — exactly the plain average of the two speeds. The difference from the previous case is the base: the speeds were held for equal times, so each speed weighs equally, and the plain mean weights them equally. The rule is symmetrical and easy to state: equal times, plain average; equal distances, harmonic average; anything else, totals.

This is why the question “what is the average of 60 and 40?” has no answer on its own. Without the base — equal distances or equal times — the phrase “average speed” is underspecified, and both 48 and 50 are defensible answers to different questions. When a textbook, a dashboard or a colleague quotes an average speed without stating the base, the first question to ask is which base was used. If nobody knows, the number is not evidence; it is a guess wearing a decimal point. The same underspecification haunts every averaged rate, from fuel economy to productivity figures, and the same cure applies: ask for the totals, and recompute.

A useful test for any claimed average speed is the round trip home. If you know the distance and the time, the average is fixed, whatever the speeds along the way were. A car that covers 100 miles in 2 hours averaged 50 mph, full stop — whether it spent an hour at 60 and an hour at 40, or twenty minutes at 80 and the rest crawling. The totals decide; the profile of speeds along the way is colour, not evidence. Hold every average-speed claim to that test and most of the misleading ones fall away on their own.

Three legs, stops and the moving average

Real trips have more than two legs, and they have stops. Take a three-leg journey: 30 miles at 30 mph, 60 miles at 60 mph and 30 miles at 45 mph, with a 20-minute stop in the middle. The driving times are 1 hour, 1 hour and 40 minutes, totalling 2 hours 40 minutes for 120 miles. The moving average — the average while actually moving — is 120 divided by 2 hours 40 minutes, which is 45 mph. Include the stop and the trip average falls: 120 miles in 3 hours is 40 mph. Both numbers are correct; they answer different questions, and quoting one without saying which is how most trip averages mislead.

The stop deserves emphasis, because it is where planning goes wrong. A delivery schedule, a race plan or a school run built on the moving average will be late by exactly the stopped time, every time. Navigation apps quote trip averages including expected stops; dashboards often quote moving averages excluding them; and the two can differ by a fifth on a trip with a long break, as here, where 45 falls to 40. When someone gives you an average speed for planning, ask whether stops are in or out — and if you are the one quoting, state it in the same breath as the number.

Multi-leg trips also expose the weighting rule at larger scale. The motorway leg covers half the distance in three-eighths of the driving time, while the town leg covers a quarter of the distance in three-eighths of the time. The slow leg’s share of time is always larger than its share of distance, which is why the average sits below the distance-weighted impression the fast leg leaves. If you remember one image from this guide, make it this: slow miles are long in time, fast miles are short, and the average counts time.

Beyond speed: rates, velocity and work

The same totals rule governs every rate, because every rate is a ratio of an amount to a time, a distance, or another base. Average rate of work is total output divided by total time: a team that assembles 120 units in 6 hours averaged 20 units per hour, whatever the hourly output was along the way. Average flow is total volume divided by total time. Average pay per hour is total pay divided by total hours — and here the trap bites in payroll disputes, where averaging two hourly rates without weighting by the hours at each rate overstates the pay of the worker whose higher rate covered fewer hours. In each case the totals decide, and the plain average of the rates is right only when the bases were equal.

Average velocity is the one near-relative that works differently, and the difference is worth knowing. Velocity has direction, so average velocity is displacement — the straight-line distance from start to finish, with sign — divided by time. Drive out 60 miles and back 60 miles and your average speed is 48 mph while your average velocity is zero, because you ended where you started. That is not a paradox; it is two different quantities. Speed answers how fast the journey was; velocity answers where it got you. Confusing them is how round trips get reported as standing still, and how one-way trips get reported as faster than they were.

Rates with money follow the same law with higher stakes. An investment that gains 10 per cent one year and loses 10 per cent the next has not averaged zero: 100 becomes 110, then 99, an average annual growth of about minus 0.5 per cent, found by the geometric mean of the growth factors, not the plain mean of the percentages. The Average Calculator page’s guide to averaging percentages makes the same point for grades and scores: percentages average cleanly only over equal bases, and over unequal bases you must rebuild the totals. Speeds are the friendliest case of the general rule, because distance and time are easy to total; the rule itself is universal.

When the simple average works — and the checklist

The simple average is not the enemy; it is the right tool for equal bases. Equal times, equal counts, equal weights — in all three cases the plain mean weights each value as it should, because the values genuinely counted equally. A class average over equal-weight tests, a daily average over equal days, a speed average over equal hours: all plain means, all correct. The error is never the plain mean itself; it is using the plain mean where the bases were unequal and pretending the weights did not matter. Learn to spot unequal bases and the trap loses its power.

Before averaging any set of speeds or rates, run this checklist. First, are the units the same — all mph, or all km/h, with no mixing? Second, what was the base: equal distances, equal times, or neither? Third, what are the totals — total distance and total time, or total output and total hours? Fourth, do stops, gaps or idle periods belong in the time or not, and have you said which? Fifth, does the result describe the journey, the work, or the direction — speed, rate, or velocity? Five questions, thirty seconds, and the average that comes out is one you can defend. The calculator above will do the arithmetic the moment the numbers are entered; the checklist is what makes the numbers worth entering.

One final caution applies to every average in this guide: an average describes the whole, never the parts. A trip averaging 48 mph may never have travelled at 48 mph for a single mile, and a worker averaging 20 units an hour may have produced 30 in one hour and 10 in the next. Averages compress; that is their job. Quote them with their totals beside them — 120 miles in 2.5 hours, not just 48 mph — and the compression stays honest, because anyone can unpack it. Without the totals, an average is a claim; with them, it is arithmetic.

Frequently asked questions

What is the formula for average speed?

Average speed equals total distance divided by total time. Add all the distances, add all the times, and divide once: 120 miles in 2.5 hours is 48 mph. Do not add the speeds and divide by how many there are — that weights each speed equally, which is only right when the times were equal.

Why is the average of 60 mph and 40 mph 48 mph and not 50 mph?

Because the slower leg takes longer. Over equal distances of 60 miles, the 60 mph leg takes 1 hour and the 40 mph leg takes 1.5 hours, so the trip is 120 miles in 2.5 hours, which is 48 mph. The plain average of 50 mph would be right only if the two speeds had been held for equal times, not equal distances.

Does stop time count in average speed?

It depends which average you mean, and you must say which. The moving average excludes stops: 120 miles in 2 hours 40 minutes of driving is 45 mph. The trip average includes them: 120 miles in 3 hours including a 20-minute stop is 40 mph. Both are correct answers to different questions; quoting one without labelling it is how trip averages mislead.

What is the difference between average speed and average velocity?

Speed is total distance divided by total time, with no direction; velocity is displacement — the straight-line distance from start to finish, with direction — divided by time. Drive out and back and your average speed is 48 mph while your average velocity is zero, because you ended where you started. Speed describes how fast the journey was; velocity describes where it got you.

Can I average speeds in mph and km/h together?

Not until you convert them to one unit. Convert every speed to miles per hour or every speed to kilometres per hour first, then apply total distance divided by total time in that unit. Averaging a number in mph with a number in km/h as if they shared a unit gives a result that belongs to no system at all.

How do I average speeds over different distances?

Use the totals: add the distances, add the times, and divide. For two equal distances there is a shortcut — twice the product of the speeds divided by their sum, which is 48 mph for 60 and 40. For unequal distances there is no shortcut that stays honest; the totals are the method, and they work for any number of legs.