Unit Conversion Mistakes with Real Consequences

Why a missing unit is dangerous

A number on its own says almost nothing. The figure 4.45 could be a force, a mass, a price or a temperature, and it only becomes meaningful when a unit is attached. Problems arise when two people, two systems or two organizations make different assumptions about the unit behind a number, and nothing in the data reveals the disagreement.

Two incidents illustrate this particularly well because both were investigated in detail and both are widely documented. Neither involved complicated mathematics. In each case, a perfectly ordinary conversion factor was missed or misapplied, and the consequences followed from there.

The Mars Climate Orbiter

NASA’s Mars Climate Orbiter launched on 11 December 1998. On 23 September 1999, contact was lost as it attempted to enter orbit around Mars, and the mission was declared lost two days later. The spacecraft was supposed to pass at an altitude of about 226 km; post-failure calculations suggested it came within about 57 km of the surface, below the 80 km thought to be the minimum for survival.

The investigation traced the cause to a unit mismatch. Ground software built by the spacecraft’s manufacturer calculated the total impulse from thruster firings and reported it in pound-force seconds, although the interface specification called for newton-seconds. NASA’s navigation software took those numbers as newton-seconds. One pound-force second is about 4.448 newton-seconds, so the thruster effects were understated by a factor of roughly 4.45. Small errors in the predicted trajectory accumulated over the months of the journey.

NASA put the combined cost of the orbiter and its companion lander mission at $327.6 million. The mishap board also found that earlier concerns raised by navigators were not acted on, so the failure was as much about process as about arithmetic. Checks that compared the ground software’s output with the specification would have exposed the mismatch before navigation depended on it.

The Gimli Glider

On 23 July 1983, Air Canada Flight 143, a Boeing 767, ran out of fuel at 41,000 feet over Ontario, on a flight from Montreal to Edmonton with a stop in Ottawa. Unlike much of the airline’s fleet, which still used pounds, this aircraft measured fuel in kilograms, and its fuel gauges were not working, so the crew relied on manual measurements of the tanks in liters.

To turn liters into mass, the crew needed the density of the fuel. The figure on the fueler’s paperwork, 1.77, was in pounds per liter, but it was used as though it were kilograms per liter. The correct value is about 0.80 kg per liter. As a result the aircraft left with roughly 10,100 kg of fuel, against about 22,300 kg required for the trip, less than half.

Both engines stopped. The crew glided the aircraft for around 17 minutes and landed at a former air force base at Gimli, Manitoba. All 69 people aboard survived, with 10 reported injuries, mostly during evacuation.

What the two cases have in common

Both errors were of the same kind: a number passed from one person or system to another without its unit being checked. In each case the data looked perfectly reasonable. A force figure that is 4.45 times too small does not look obviously wrong, and neither does a fuel density of 1.77.

Both also lacked an independent check. In the glider case, a quick comparison of the fuel loaded with the amount normally needed for the route would have shown a large shortfall. In the orbiter case, the data were consumed by another system that had no way to know a different unit had been used. Finally, both happened in settings where two measurement systems were in use side by side, which is exactly when mistakes become more likely. The arithmetic was easy; the failure was in assuming that everyone meant the same unit.

Practical defenses

The lessons apply well beyond aerospace, down to a spreadsheet or a shopping list:

• Write the unit next to every number, in labels, file headers and messages, not just in your head.
• Agree on one unit system for each project and say so in the specification.
• Convert once, in one place, using exact documented factors.
• Check the result for plausibility: is the order of magnitude what you would expect?
• Have someone else, or something else, verify critical numbers independently.

Plausibility checks are cheap and powerful. A mass that is about half or double what you expected is often a sign that a unit has been mixed up, since the pound-to-kilogram factor is about 2.2 and the mile-to-kilometer factor about 1.6.

Takeaways for everyday conversions

Most people will never handle spacecraft or airliners, but the same habits prevent smaller errors: a recipe in cups mistaken for milliliters, a package weight entered in pounds instead of kilograms, or a distance in miles read as kilometers. A unit converter such as this one helps by showing the full equation, including both units, so you can see exactly what was converted into what.

For anything where health, safety or large sums depend on the result, a converter is a check, not an authority. Confirm the figures against the original document or specification, and verify the units before you trust a number.