Solve for Speed, Distance, or Time - fill in any two values and the third is solved instantly.
The three most fundamental quantities in everyday motion are speed, distance, and time. They are bound together by one of the simplest and most useful equations in physics - the Distance Formula. Understanding this relationship allows you to answer questions like "How long will my drive take?", "How far did I run?", or "How fast was I going?" without any guesswork. The formula works for anything that moves: cars, runners, aircraft, ships, and even light.
These three equations are really the same formula rearranged. Once you know any two of the three values, you can always solve for the third. This calculator automates that algebra for you - just fill in two boxes and the answer appears instantly. The variable $v$ represents velocity (or speed), $d$ represents distance, and $t$ represents time.
Speed is a scalar quantity - it tells you how fast something is moving but says nothing about direction. For example, "60 mph" is a speed. Velocity, on the other hand, is a vector quantity that combines speed with a specific direction. "60 mph heading north" is a velocity. In everyday navigation and this calculator, we work primarily with speed. However, in physics and engineering, velocity matters because direction changes can affect calculations even when the rate of movement stays the same - think of a car driving in a circle at constant speed: its speed is constant, but its velocity changes every instant because the direction keeps shifting.
Constant speed means the rate of movement never changes throughout the entire journey - rare in real life but useful for simple calculations. Average speed is the practical equivalent: it is the total distance divided by the total time elapsed, regardless of how many stops, accelerations, or slowdowns occurred along the way. If you drive 120 miles in 2 hours, your average speed was 60 mph - even if you sat in traffic for 20 minutes or reached 80 mph on the highway. This calculator computes average speed unless you are measuring a specific segment at a genuinely constant rate. The formula for average speed is: $\bar{v} = \frac{d_{total}}{t_{total}}$
Pace is simply the inverse of speed, expressed as time per unit distance rather than distance per unit time. Where a runner's speed might be 6 miles per hour (mph), their pace would be 10 minutes per mile - meaning it takes them 10 minutes to cover one mile. Pace is the preferred metric in running communities because it directly answers the question "How long will each mile take me?" rather than the less intuitive "How many miles will I cover each hour?"
The conversion is: $\text{Pace (min/mile)} = \frac{60}{\text{Speed (mph)}}$ and $\text{Pace (min/km)} = \frac{60}{\text{Speed (km/h)}}$
So a runner at 8 mph has a pace of $\frac{60}{8} = 7.5$ minutes per mile, or 7 minutes and 30 seconds per mile. A 5-minute-per-kilometer pace corresponds to 12 km/h. This calculator displays both metrics automatically whenever speed is known.
For a road trip with stops, the average speed depends on whether you include or exclude the stopped time. There are two useful interpretations:
1. Moving average speed - total distance divided by only the time the vehicle was actually moving. This tells you how fast you drove when driving.
2. Overall average speed (door-to-door) - total distance divided by the entire elapsed time including stops. This is the number most relevant for planning: if you drove 300 miles in 5 total hours (including a 30-minute lunch stop), your door-to-door average speed was $\frac{300}{5} = 60$ mph.
This calculator uses the total time you input, so enter the full elapsed time (including stops) if you want the door-to-door average.
One mile equals exactly 1.60934 kilometers, so the conversion factors are:
$\text{mph} = \frac{\text{km/h}}{1.60934}$ and $\text{km/h} = \text{mph} \times 1.60934$
A quick mental shortcut: multiply mph by 1.6 to get approximate km/h, or divide km/h by 1.6 to get approximate mph. Some useful benchmarks to memorize:
- 60 mph = 96.6 km/h (roughly 100 km/h, a common highway limit)
- 100 km/h = 62.1 mph
- 30 mph = 48.3 km/h (a typical urban speed limit)
- 1 m/s = 3.6 km/h = 2.237 mph (useful in science contexts)
The converter above performs all these transformations simultaneously so you never need to do them by hand.
A knot (abbreviated "kts" or "kt") is a unit of speed equal to one nautical mile per hour. One nautical mile is defined as exactly 1,852 meters, which corresponds to one minute of arc of latitude along the Earth's surface. This makes knots especially natural for navigation because chart distances are measured in nautical miles.
Conversions: $1 \text{ knot} = 1.15078 \text{ mph} = 1.852 \text{ km/h}$
Knots are the standard unit in maritime navigation (ships and boats), aviation (aircraft airspeed and wind speed), and meteorology (wind speed in weather forecasts). If you see wind reported at 20 knots, that is about 23 mph or 37 km/h. Most commercial aircraft cruise around 450-500 knots (roughly 520-575 mph).
Starting from the distance formula $d = v \times t$, divide both sides by $v$ to isolate time:
$$t = \frac{d}{v}$$
For example: you need to drive 250 miles at an average speed of 65 mph. Time equals $\frac{250}{65} \approx 3.846$ hours. To convert the decimal to hours and minutes, take the fractional part $0.846 \times 60 \approx 50.8$ minutes - so roughly 3 hours and 51 minutes.
This calculator handles all of that automatically: it displays the solved time broken into hours, minutes, and seconds so there is no mental arithmetic required. Just enter the distance and speed, and the time field populates immediately.