Unit conversion: the complete guide (SI, imperial, pitfalls and 2019 redefinition)

Why so many different units?

Before the 19th century, every region, town, and trade guild had its own units of measurement. In England, the "foot" varied by locale. The "pound" meant different things to a merchant, a physician, and a gunsmith. A carpenter buying timber 50 miles from home had to perform mental unit conversions at every transaction. Commerce, science, and engineering all suffered from this fragmentation.

The French Revolution provided the occasion for a radical reform. In 1795, France officially adopted the metre, defined as one ten-millionth of the distance from the North Pole to the equator along the Paris meridian. The geodesic survey itself carried some imprecision, but the principle was revolutionary: a unit grounded in a natural constant rather than an arbitrary object.

International standardisation accelerated with the Metre Convention, signed on 20 May 1875 in Paris by seventeen founding states. It created the Bureau International des Poids et Mesures (BIPM), based in Sèvres, France, tasked with maintaining international measurement standards. The 20th of May has since been celebrated as World Metrology Day.

A lesser-known historical footnote: even France was not always a model of consistency. Napoleon, who exported the metric system across conquered Europe, eventually allowed some traditional units to return during the Restoration — a brief retrograde step that lasted until the metric system was definitively reinstated by law in 1840. Consistency in measurement, it turns out, is a political achievement as much as a scientific one.

The International System of Units (SI)

The International System of Units (SI), adopted by the General Conference on Weights and Measures (CGPM) in 1960 and governed by ISO 80000, rests on seven independent base units from which all other units are derived.

Key derived units

From these seven building blocks, the SI constructs a coherent set of derived units, all expressible without numerical factors within the base system:

• Newton (N): force — 1 N = 1 kg·m/s² (force that accelerates 1 kg by 1 m/s²)
• Pascal (Pa): pressure — 1 Pa = 1 N/m² (atmospheric pressure ≈ 101,325 Pa)
• Joule (J): energy — 1 J = 1 N·m = 1 kg·m²/s²
• Watt (W): power — 1 W = 1 J/s
• Hertz (Hz): frequency — 1 Hz = 1 cycle/s
• Coulomb (C): electric charge — 1 C = 1 A·s
• Volt (V): electric potential — 1 V = 1 W/A
• Ohm (Ω): electric resistance — 1 Ω = 1 V/A
• Tesla (T): magnetic flux density — 1 T = 1 kg/(A·s²)

The historic 2019 redefinition

On 20 May 2019 — a date symbolically chosen to coincide with the anniversary of the Metre Convention — the SI underwent its most profound revision since 1960. The 26th General Conference on Weights and Measures (CGPM) voted unanimously to redefine four base units.

The problem with the Sèvres kilogram

Since 1889, the kilogram had been defined by a physical object: the International Prototype of the Kilogram (IPK), a cylinder 39 mm in diameter and height, made of platinum-iridium alloy (90/10), stored under three glass bells in the Pavillon de Breteuil at Sèvres. Every kilogram in the world was ultimately a copy of this cylinder.

The problem: the IPK drifted. During periodic comparisons with its official copies (the "witness" cylinders), discrepancies of approximately 50 micrograms had accumulated over a century. In other words, the very definition of the kilogram was not stable. For high-precision metrology — quantum physics, Planck constant measurements, watt-balance experiments — this was unacceptable.

The solution: fundamental constants

The solution adopted in 2019 was elegant: fix the numerical values of universal physical constants, and derive the units from them. For the kilogram, the Planck constant h is now exactly 6.626 070 15 × 10⁻³⁴ J·s. The kilogram is the mass that gives this value of h when used in the relevant quantum mechanical equations.

The four units redefined in 2019:

• Kilogram: via the Planck constant h
• Ampere: via the elementary charge e = 1.602 176 634 × 10⁻¹⁹ C
• Kelvin: via the Boltzmann constant k = 1.380 649 × 10⁻²³ J/K
• Mole: via the Avogadro constant N_A = 6.022 140 76 × 10²³ mol⁻¹

The major consequence: all SI units are now defined by universal constants that are invariant anywhere in the universe, reproducible in any suitably equipped laboratory. No physical artefact is required. The Sèvres prototype is now a museum exhibit. For everyday life, nothing changed. For the physicist measuring to 14 significant figures, it was a revolution.

Imperial and US Customary: why three countries resist

As of 2026, three countries have not officially adopted the SI as their primary system: the United States, Liberia, and Myanmar. This resistance has historical, economic, and political roots.

The United States: a metric transition that stalled

The Metric Conversion Act of 1975 declared SI the "preferred" system of the United States and created the Metric Board. But the Board was dissolved in 1982, starved of funding and facing opposition from established industries (construction, food, agriculture). In 1988, the Omnibus Trade Act made SI mandatory for federal agencies — with permanent exemptions for consumer commerce. Result: American engineers frequently work in SI; food labels show both systems; consumers remain on customary units. The US military and most scientific institutions use SI exclusively.

Imperial vs US Customary: the hidden divergence

A frequent mistake: imperial and US Customary are not the same. They share the same names (gallon, pint, ounce) but the values differ significantly:

Mars Climate Orbiter: $327 million into thin air

On 23 September 1999, NASA's Mars Climate Orbiter was destroyed in the Martian atmosphere because of a unit confusion. The Lockheed Martin team (software developer) was transmitting thruster force data in pound-force·seconds (lbf·s), while NASA's navigation software expected newton·seconds (N·s). One newton·second = 0.2248 lbf·s. Over months of trajectory corrections, the error accumulated and the probe entered an orbit too low — estimated at 57 km altitude instead of the intended 150 km — causing it to break up. Cost of the mission: $327 million. Root cause: no unit verification at the software interface between the two teams. NASA published a full post-mortem (JPL Internal Report D-16496, November 1999) that became an industry reference on interface documentation standards.

Lengths and distances

Length conversions are among the most frequent in daily life. All the equivalences below are exact by definition, anchored either in the SI definition of the metre or in the 1959 international agreements:

Note: the nautical mile has been defined as exactly 1,852 m since the 1929 International Hydrographic Conference in Monaco. It corresponds approximately to one arc-minute of latitude along the Earth's meridian — hence its navigational utility: 1 knot = 1 nautical mile per hour.

Mass vs weight: the classic confusion

One of the most frequent errors in science — and in everyday life — is conflating mass and weight. They are not the same physical quantity.

Mass (kg) is an intrinsic property of matter: it measures the amount of matter and its resistance to acceleration (inertia). It is the same on Earth, on the Moon, and in deep space. An astronaut with a mass of 80 kg has a mass of 80 kg in orbit.

Weight (N) is the gravitational force acting on a mass. It varies with the local gravitational acceleration g. The standard value adopted by the CGPM is g = 9.80665 m/s² — but g actually varies from 9.764 m/s² at the equator (centrifugal effect + larger radius) to 9.863 m/s² at the poles. The difference reaches 0.5%, measurable with precision scales.

The relationship: Weight (N) = Mass (kg) × g (m/s²)

On Earth: 1 kg ≈ 9.807 N. On the Moon (g ≈ 1.62 m/s²): 1 kg ≈ 1.62 N. In interstellar space: 1 kg = 0 N (weightlessness).

Pound-mass vs pound-force

In US Customary, the pound (lb) is officially a unit of mass (1 lb = 0.453 592 37 kg exactly). But in traditional Anglo-Saxon engineering, the pound-force (lbf) is the gravitational force exerted on a pound-mass under standard gravity. This ambiguity — the same word for two different physical quantities — is one of the most persistent sources of error in international engineering. The density of aviation fuel is approximately 0.803 kg/L but 1.77 lb/L: mixing these without conversion is exactly how Air Canada Flight 143 ran out of fuel mid-flight in 1983.

Temperature: the offset trap

Temperature conversion is special because, unlike length or mass, it involves an additive offset in addition to a multiplicative factor. This two-parameter conversion consistently catches non-experts off guard.

The four temperature scales

Conversion formulas

• °C → °F: °F = °C × 9/5 + 32
• °F → °C: °C = (°F − 32) × 5/9
• °C → K: K = °C + 273.15
• K → °C: °C = K − 273.15
• °F → °R: °R = °F + 459.67
• K → °R: °R = K × 9/5

Key reference points

Reference temperatures to memorise: 37 °C = 98.6 °F (normal human body temperature); −40 °C = −40 °F (the crossover point where the two scales meet); 0 K = −273.15 °C (absolute zero, the theoretical lower limit of temperature); 273.16 K = 0.01 °C (triple point of water, used as a calibration reference).

A widespread style error: you say "273 kelvin" or "273 K", never "273 degrees kelvin" or "273 °K". The kelvin is an SI base unit, not a relative temperature graduation — unlike the degree Celsius, which is a temperature difference or interval. This distinction is enforced by the BIPM and the NIST (NIST Special Publication 330).

Our online unit converter handles all these formulas with full decimal precision, including conversions across all four temperature scales.

Volume and capacity: the great gallon confusion

Volume is arguably the domain where conversion errors are most costly — particularly for recipes, fuel, and industrial chemicals.

SI units

The cubic metre (m³) is the SI base unit of volume. The litre (L) is a legal unit (not strictly SI but accepted): 1 L = 1 dm³ = 0.001 m³. The millilitre equals exactly 1 cm³ (also written cc), which makes it practical in medicine and chemistry.

Gallons and pints: disambiguation table

Area

The SI unit for area is the square metre (m²). For land and agricultural contexts, the hectare (ha) = 10,000 m² is used universally alongside SI.

• Are (a): 100 m² — used in some European land registry documents
• Hectare (ha): 10,000 m² = 100 ares
• Acre: 4,046.86 m² ≈ 0.405 ha — USA, UK, English-speaking Canada
• Square foot (ft²): 0.0929 m² — US real estate listings
• Township: 93.24 km² = 36 one-square-mile sections — US cadastral subdivision

Speed

The SI unit for speed is the metre per second (m/s). In practice, several units coexist depending on the domain:

• km/h: road transport in most countries. 1 km/h = 1/3.6 m/s ≈ 0.2778 m/s
• mph (miles per hour): road transport in USA and UK. 1 mph = 1.60934 km/h
• Knot (kn): international maritime and aviation. 1 kn = 1 NM/h = 1,852 m/h ≈ 1.852 km/h
• Mach: ratio to the local speed of sound. Mach 1 ≈ 340 m/s at 15 °C at sea level, but varies with temperature and altitude (Mach 1 at 10,000 m ≈ 295 m/s). Mach is not a fixed constant — always specify conditions.
• c (speed of light in vacuum): 299,792,458 m/s exactly — this value is fixed by definition since 1983, as it is used to define the metre.

Computer data: SI kilo or binary kibi?

This is one of the most common misconceptions in consumer computing, and a regular source of disappointment when purchasing hard drives or memory cards.

The prefix problem

In SI, kilo = 10³ = 1,000, mega = 10⁶, giga = 10⁹, tera = 10¹². These are powers of ten. In computing, engineers historically used the nearest powers of two: 2¹⁰ = 1,024 ≈ 1,000, and called this "kilo". The confusion was tolerable when the gaps were small. It became unacceptable at terabyte scale.

In practice: hard drive manufacturers sell in GB (= 10⁹ bytes, SI). Windows reports in GiB (= 2³⁰ bytes, IEC). A 1 TB drive (manufacturer) = 1,000,000,000,000 bytes. Windows divides by 2³⁰: 1,000,000,000,000 ÷ 1,073,741,824 ≈ 931.32 GiB — hence the 931 GB displayed. macOS has displayed in decimal GB since version 10.6 (Snow Leopard, 2009), aligning with manufacturer labelling.

The IEC 80000-13 standard (published by the International Electrotechnical Commission, 2008) introduced kibi, mebi, gibi, and tebi prefixes to disambiguate, but their adoption in operating systems and consumer interfaces remains partial as of 2026. Linux, many professional tools, and the NIST now use them consistently.

Bits vs bytes

Another common confusion: network speeds are usually quoted in bits per second (Mb/s, Gb/s), while file sizes are in bytes (MB, GB). 1 byte = 8 bits. A theoretical 1 Gb/s fibre connection downloads at approximately 125 MB/s (1,000 Mb/s ÷ 8 = 125 MB/s). The gigabit-to-gigabyte conversion divides by 8 — always apply this when interpreting ISP marketing claims.

Energy

Energy appears in radically different contexts — nutrition, physics, electricity, oil — with wildly different units depending on the field.

A common nutrition confusion: food labels often show "Calories" with a capital C. These are kilocalories (kcal). A 500 kcal chocolate bar provides 500 × 4,184 = 2,092,000 J ≈ 2.09 MJ of chemical energy. To put that in perspective: one watt-hour = 3,600 J, so that bar contains roughly 581 Wh — enough to power a 10 W LED bulb for nearly 58 hours.

Practical conversions you need

Travelling in the United States

• Fuel: 1 US gallon ≈ 3.785 L. Price in $/gallon ÷ 3.785 = $/L
• Speed: 60 mph ≈ 97 km/h; 100 km/h ≈ 62 mph
• Temperature: 77 °F = 25 °C (pleasant day); 32 °F = 0 °C (freezing)
• Height: 6 feet = 182.9 cm; 5'10" = 177.8 cm
• Weight: 150 lb = 68 kg; 1 lb = 0.4536 kg

UK recipes and cooking

• 1 US cup = 236.6 ml; 1 UK cup = 284.1 ml
• 1 US tablespoon = 14.79 ml; 1 UK tablespoon = 17.76 ml
• 1 ounce (mass) = 28.35 g
• 1 pound (lb) = 16 oz = 453.6 g

International engineering

When converting specifications between systems, the SAW TOOLS scientific calculator handles expressions with exponents and powers of ten, essential for large-magnitude conversions. For projects involving colour spaces and optical measurement instruments (some of which use non-SI colorimetric units), our colour converter covers RGB, HSL, HSV, CMYK, and HEX spaces.

Conversion errors that made history

The history of engineering and aviation is punctuated by accidents caused by unit confusion. These incidents led to profound changes in documentation and verification practices.

Mars Climate Orbiter (NASA, 1999)

The probe was designed to study the Martian climate from a stable orbit at approximately 150 km altitude. On 23 September 1999, during orbital insertion, navigation data showed the spacecraft entering the atmosphere at an altitude of around 57 km — far too low, causing its destruction. The investigation established that the navigation sub-system built by Lockheed Martin (Sunnyvale, California) was transmitting thruster force data in pound-force·seconds, while NASA JPL's flight navigation software expected newton·seconds. Conversion factor: 1 lbf·s = 4.448 N·s. The error was not in the software itself, but in the complete absence of unit documentation and validation at the interface between the two teams. NASA issued a directive mandating explicit unit labelling in all software interfaces. Mission cost: $327.6 million.

Gimli Glider — Air Canada Flight 143 (1983)

On 23 July 1983, a Boeing 767 departed Montreal for Edmonton with a critically miscalculated fuel load. The ground crew calculated the required fuel in pounds, but the fuelling was carried out using kilograms without conversion. The fuel density constant (approximately 1.77 lb/L) had been used where the kg/L equivalent (0.803 kg/L) was required. The aircraft departed with less than half the required fuel. At cruising altitude — 12,500 metres over northern Ontario — both engines flamed out simultaneously. Captain Robert Pearson, an experienced glider pilot, successfully landed the 100-tonne powerless aircraft on the decommissioned Gimli airbase in Manitoba. All 61 passengers and 8 crew members survived. The aircraft, nicknamed the "Gimli Glider", is one of the most documented emergency landings in aviation history.

Korean Air Cargo Flight 6316 (2000)

On 15 April 2000, a Boeing 747 freighter operated by Korean Air crashed shortly after take-off from Shanghai Hongqiao Airport. The investigation found that the crew had misinterpreted the recommended takeoff thrust setting: engineers had transmitted the reference pressure parameters in inches of mercury (a unit used in Korean procedures at the time), but the crew interpreted the figure as if it had been multiplied by a factor of ten — resulting in a grossly insufficient takeoff thrust. Three crew members and residents on the ground were killed. The accident accelerated the international standardisation of units in civil aviation documentation and preflight briefings.

Conclusion: converting with rigour

Unit conversion is not a trivial mathematical exercise. Behind every conversion table lie historical conventions, political compromises, evolving definitions, and subtle distinctions (imperial vs US Customary, SI vs IEC, mass vs weight) that continue to trip up experienced engineers.

The professional best practice is systematic: always document units in data exchanges, never assume that a bare number uses the "obvious" system, and verify critical conversions against a primary reference source (BIPM, NIST SP 330, ISO 80000).

For your everyday conversion needs — lengths, masses, temperatures, volumes, speeds, areas, data — our online unit converter covers all the categories described in this guide, with no intrusive advertising and no personal data collection.