Unit Conversion Disasters: The Mars Orbiter, the Gimli Glider and What They Teach
A lost Mars orbiter, an airliner that ran dry at 41,000 feet, and a snapped axle. What went wrong, and the habits that prevent the same class of error.
Introduction
A unit conversion error does not announce itself. It produces a number that looks entirely reasonable, sits in the right column, passes every sanity check a tired person is likely to apply, and only reveals itself when something physical goes wrong.
That is what makes the well-documented cases worth studying. None of them involved anyone failing at arithmetic. In every case the multiplication was performed correctly - on the wrong assumption about what the number meant. This guide walks through three of the clearest examples, the version that still happens weekly in hospitals, and the practices that actually prevent them.
The Mars Climate Orbiter, 1999
NASA lost a Mars orbiter because two pieces of software disagreed about a unit, and nothing in the process was designed to notice.
The spacecraft fired its thrusters regularly to manage momentum, and the ground software that processed those firings reported the resulting impulse in pound-force seconds. The navigation software receiving those figures expected newton-seconds. One pound-force second is 4.448 newton-seconds, so every value arriving at the navigation model was roughly four and a half times smaller than reality.
No single number was absurd enough to trigger an alarm. The error accumulated quietly across a nine-month cruise, gradually shifting the predicted trajectory. When the orbiter arrived in September 1999 it was aiming for a closest approach of about 226 kilometres above the surface. It actually came in near 57 kilometres, far too deep in the atmosphere for a spacecraft to survive, and contact was lost.
The review board's finding is the part worth carrying away. The mismatch was the immediate cause, but the deeper failure was that no checkpoint existed where the two systems' assumptions were ever compared. The units were documented. Nobody had built a step that verified them.
Newtons and pounds-force remain one of the most confusable pairs in engineering, which our guide to newtons and pounds-force covers in more detail.
The Gimli Glider, 1983
Air Canada Flight 143 ran out of fuel at 41,000 feet because of a density figure.
Canada was midway through converting to metric, and the Boeing 767 was among the first Air Canada aircraft to measure fuel in kilograms rather than pounds. The aircraft's fuel gauges were inoperative, so the crew measured the tanks manually with a dipstick, which gives a volume in litres. Converting litres to a mass requires multiplying by the fuel's density.
The figure they used was 1.77, which is the density of jet fuel in pounds per litre. The number they needed was 0.803, the density in kilograms per litre.
The consequences follow directly from that single substitution:
- The 7,682 litres already aboard were really 6,169 kg of fuel.
- The 1.77 figure made it look like 13,597 - a number in pounds, read as kilograms.
- The flight required 22,300 kg, so they should have added about 20,000 litres.
- Working from the wrong figure, they added roughly 4,900 litres.
The aircraft departed with about 45 percent of the fuel it needed, and every gauge and calculation agreed it was full. The engines failed over Ontario. Captain Robert Pearson, who happened to be an experienced glider pilot, flew the powerless 767 to a former air force base at Gimli, Manitoba, part of which was in use that day as a drag strip. The nose gear collapsed on landing. Nobody was killed.
The lesson here is subtler than "check your units". A density figure is not a pure conversion factor - it silently converts between volume and mass, which means the units on both sides have to be right. Our guide to kilograms and pounds covers the mass side of that pairing.
Tokyo Disneyland Space Mountain, 2003
In December 2003 an axle on a Space Mountain train snapped mid-ride. Nobody was injured, but the investigation exposed a failure mode that engineering organisations should find genuinely alarming.
The specification drawings had been converted from imperial to metric units in 1995. A parts order placed years later was worked from the pre-conversion figures, producing an axle 44.14 mm in diameter where the design called for 45 mm.
The shortfall was 0.86 millimetres - under a millimetre, and far too small to notice by eye or catch in handling. It was enough to allow excess play, and over enough cycles that play became a fatigue failure. This is the most unsettling case of the three, because the error was not a factor of 4.45 or a factor of two. It was under two percent, and it still ended in a broken component.
The Version That Still Happens Every Week
The historical cases get retold because they are dramatic. The same error class causes far more harm in ordinary settings, where nobody writes a report about it.
Weight in medicine
Many drug doses are calculated per kilogram of body weight. If a patient weighing 70 kilograms is recorded as 70 pounds, the recorded weight is 31.8 kg - 55 percent below reality - and every dose derived from it is wrong in the same proportion. The error runs the other way too, and the risk is greatest for children, where doses are almost always weight-based and body weights are small enough that the resulting figure still looks plausible.
This is why patient safety organisations have pushed for years to record weights in kilograms only, and to remove pounds from scales and charts entirely. The fix is not better arithmetic; it is eliminating the opportunity for the wrong unit to be entered at all.
Milligrams and micrograms
A milligram is a thousand micrograms. Confusing the two produces a thousandfold error in either direction, and the abbreviations are visually similar in handwriting - which is precisely why "mcg" is now preferred over the Greek symbol on prescriptions. Our guide to micrograms and milligrams covers where the boundary sits.
What These Cases Have in Common
Four patterns run through all of them.
The wrong answer looked reasonable. Not one of these errors produced an obviously absurd number. A quantity that is 4.45 times too small, or 45 percent of what it should be, still sits comfortably in the expected range. Plausibility is not validation.
The unit lived outside the number. In every case the value was passed between people or systems as a bare figure, with the unit held somewhere else - in a document, a convention, or an assumption. The moment a number travels without its unit attached, the error becomes possible.
A transition period created the gap. Canada was mid-metrication. Disney had changed its drawings but not retired the old ones. Two NASA teams worked to different conventions. Migrations are when these failures cluster, because both systems are briefly valid at once.
Nothing was designed to catch it. This is the common thread that matters most. Every one of these organisations employed careful people. What was missing was a step whose specific job was to verify the unit, rather than to recompute the arithmetic.
How to Avoid the Same Class of Error
- Never let a number travel without its unit. Label spreadsheet columns, variable names and interface fields with the unit, not just the quantity. Write fuel_kg, not fuel.
- Check the magnitude, not just the maths. Ask whether the answer is the right size before checking whether the multiplication was right. Most unit errors are off by 2, 4.45, 1,000 or 2.2 - all recognisable once you look for them.
- Convert once, at a boundary. Pick one internal unit, convert on the way in and on the way out, and never mix conventions in the middle. Rounding and unit errors both compound when a value is converted repeatedly, as our guide to significant figures and rounding explains.
- Be most careful during a transition. If two conventions are live at once, treat every figure crossing between them as suspect until confirmed.
- Verify the assumption, not the calculation. Re-running the arithmetic confirms nothing if the input meant something else. Ask what the number is before asking whether it is correct.
Conclusion
A spacecraft, an airliner and a roller coaster failed for the same reason: a number arrived somewhere carrying a different meaning from the one expected, and nothing in the process was built to notice. The arithmetic was never the weak point.
Keep units attached to values, sanity-check the size of an answer before trusting it, and treat any conversion between systems as a place where verification belongs. Our newtons to pounds-force converter and kilograms to pounds converter handle the two pairings behind the first two stories on this page.