Running Pace, Fuel Efficiency, and Everyday Physics Formulas

A runner finishes a marathon in 3 hours and 30 minutes. Was that fast? It depends — do you think in minutes per mile, minutes per kilometre, or kilometres per hour? The same speed can feel impressive or mediocre depending on the unit. Behind every pace, fuel efficiency, or travel time calculation sits one deceptively simple equation: speed = distance / time.

The speed-distance-time triangle

The relationship speed = distance / time can be rearranged three ways. Cover the variable you want to find and the remaining two show you the operation:

speed    = distance / time
distance = speed × time
time     = distance / speed

Example: 150 km at 60 km/h
time = 150 / 60 = 2.5 hours = 2 h 30 min

Unit conversions

The most common source of errors is mixing units. Memorise two conversions and derive the rest:

• 1 mile = 1.60934 km — so multiply mph by 1.609 to get km/h
• 1 km = 0.62137 miles — the inverse

Running pace math

Runners measure speed as pace (time per distance) rather than speed per hour. A 4:00 min/km pace means it takes exactly 4 minutes to cover one kilometre. To convert pace to speed: speed (km/h) = 60 / pace (min/km). So a 4:00 pace = 15 km/h.

Negative splits

A negative split means running the second half faster than the first. Most world records are set with negative or even splits. Starting too fast depletes glycogen early — the body hits “the wall” around 30 km in a marathon. A conservative first half preserves fuel for a stronger finish.

Fuel efficiency: MPG vs L/100km

The US measures fuel efficiency in miles per gallon (MPG) — bigger is better. Most of the world uses litres per 100 kilometres (L/100km) — smaller is better. These are inverse relationships, which creates a surprising effect:

Converting between units:
L/100km = 235.215 / MPG
MPG     = 235.215 / (L/100km)

Examples:
30 MPG = 235.215 / 30 = 7.84 L/100km
8 L/100km = 235.215 / 8 = 29.4 MPG

Fuel cost per trip

The calculation is straightforward: find how much fuel you need, then multiply by the price.

fuel needed = distance / efficiency
total cost  = fuel needed × price per unit

Example (metric):
400 km trip, car does 8 L/100km, fuel costs $1.50/L
fuel = (400 / 100) × 8 = 32 litres
cost = 32 × $1.50 = $48.00

Example (imperial):
250 miles, 30 MPG, gas at $3.50/gal
fuel = 250 / 30 = 8.33 gallons
cost = 8.33 × $3.50 = $29.17

Why units matter

• NASA's Mars Climate Orbiter crashed in 1999 because one team used pounds of force and another used newtons. A $327 million unit conversion error.
• Air Canada Flight 143 ran out of fuel mid-flight in 1983 because ground crew confused kilograms and pounds when calculating fuel load.

The physics is simple — speed equals distance over time. The difficulty is always in the units. Get those right and the rest follows.