Why not just use one conversion factor per pair?

Pair-wise factors would mean storing ~N² factors per category where N is the number of units — and would inevitably accumulate small rounding errors as we picked which way to round each factor. The hub-and-spoke approach stores N exact factors and computes pairs at runtime, so cm → inches and inches → cm always round-trip exactly.

Are temperatures special?

Yes. Length, weight, energy, volume are all multiplicative — you scale by a factor. Temperature is affine — Fahrenheit and Celsius have different zero points, so the conversion involves both a factor and an offset. We store an offset alongside the factor for the temperature category specifically.

Why IEEE 754 floats and not arbitrary precision?

IEEE 754 double precision gives roughly 15-17 significant digits of accuracy, more than every measurement on the page has to begin with. The factors themselves are stored at full source-table precision; the only loss happens at the final display where we round to a sensible number of decimal places for the unit involved.

Methodology

Units methodology

NIST SP 811, BIPM SI Brochure, and the 1959 yard-and-pound agreement — under the hood.

Convertitive’s 11 unit-conversion categories — length, weight, temperature, volume, speed, time, pressure, energy, power, data, torque — share a single architecture: every unit is stored as a conversion factor against a canonical SI base unit, and every pair conversion goes through that base. This page walks through how the factors are sourced, where the precision limits sit, and the one category that doesn’t fit the pattern (temperature).

The SI base units

Every unit on the site reduces to one of the seven SI base units defined in the BIPM SI Brochure (9th edition, 2019):

Length — metre (m)
Mass — kilogram (kg)
Time — second (s)
Temperature — kelvin (K)
Amount of substance — mole (mol)
Electric current — ampere (A)
Luminous intensity — candela (cd)

Derived units (newton, joule, watt, pascal, etc.) are algebraic combinations of those seven. Our energy and power categories use joule and watt as their canonical anchors; pressure uses pascal; torque uses newton-metre.

The hub-and-spoke architecture

Each unit in a category stores one number: its conversion factor relative to the category’s canonical SI base unit. To convert from unit A to unit B in the same category:

result = value × factorA / factorB

Concretely, in our length registry inches have factor 0.0254 (1 inch = 0.0254 m) and centimetres have factor 0.01. Converting 5 cm to inches is 5 × 0.01 / 0.0254 ≈ 1.9685. Reverse direction: 1.9685 × 0.0254 / 0.01 = 5.00000…. Round-trips exactly because the same factors are used in both directions.

Where the factors come from

NIST Special Publication 811

The US National Institute of Standards and Technology publishes SP 811: Guide for the Use of the International System of Units (SI). It’s the canonical reference for US-specific units (foot, pound, gallon, BTU, horsepower) expressed in SI. Most of our imperial / US-customary factors come from this document and have been valid since the 1959 international yard and pound agreement.

1959 international yard and pound agreement

Signed by the US, UK, Canada, Australia, South Africa, and New Zealand on 1 July 1959. Set the inch at exactly 0.0254 metres and the pound at exactly 0.45359237 kilograms. These are exact rational numbers, not approximations — every imperial-metric conversion that uses these factors is exact until the final display rounding.

BIPM SI Brochure

The International Bureau of Weights and Measures (Bureau International des Poids et Mesures) publishes the SI Brochure, the canonical definition of the metric system. We follow the 9th edition (2019), which moved several base units to definitions in terms of fundamental physical constants. The kilogram, for example, is now defined via the Planck constant rather than a metal artefact in a vault outside Paris.

Temperature — the affine outlier

Length, weight, volume, etc. scale linearly: zero in one unit is zero in every other unit. Temperature doesn’t — 0°C is 32°F, 0°F is roughly −17.78°C. The conversions require both a factor and an offset, which we store as a tuple:

result = (value − offsetFrom) × factorFrom / factorTo + offsetTo

Concretely: Fahrenheit has factor 5/9 against kelvin and offset 459.67; Celsius has factor 1 against kelvin and offset 273.15. The conversion formula reduces to the familiar °F = °C × 9/5 + 32 once the offsets resolve. See our Celsius vs Fahrenheit comparison for the historical context.

The precision floor

Every conversion runs in IEEE 754 double precision, which provides about 15-17 significant decimal digits. The factors themselves are stored exact (rational numbers where possible, decimal approximations where the source-table itself uses decimals), so the limiting factor is always the display:

Length, weight, volume: 6 significant figures.
Temperature: 2 decimal places.
Energy, power: 4-6 significant figures depending on the unit.
Time: exact integers where possible (1 hour = exactly 3600 seconds); otherwise 6 figures.

For any input that would expose floating-point edge cases (extremely large or small values), the result is still correct to within ε of the true value — but you should use a dedicated arbitrary-precision tool for anything that needs more than 15 digits of accuracy.

What this means for citation

Convertitive’s unit conversions are derived from published, public-domain factors. When citing a Convertitive result for any defensible purpose:

The numerical result is exact within IEEE 754 limits.
The source authority is NIST SP 811, BIPM SI Brochure, or the 1959 international yard and pound agreement.
Display rounding is the only place precision is lost; you can request a tighter representation by using the REST API endpoint, which returns the unrounded double.

Frequently asked questions

Why not just use one conversion factor per pair?: Pair-wise factors would mean storing ~N² factors per category where N is the number of units — and would inevitably accumulate small rounding errors as we picked which way to round each factor. The hub-and-spoke approach stores N exact factors and computes pairs at runtime, so cm → inches and inches → cm always round-trip exactly.
Are temperatures special?: Yes. Length, weight, energy, volume are all multiplicative — you scale by a factor. Temperature is affine — Fahrenheit and Celsius have different zero points, so the conversion involves both a factor and an offset. We store an offset alongside the factor for the temperature category specifically.
Why IEEE 754 floats and not arbitrary precision?: IEEE 754 double precision gives roughly 15-17 significant digits of accuracy, more than every measurement on the page has to begin with. The factors themselves are stored at full source-table precision; the only loss happens at the final display where we round to a sensible number of decimal places for the unit involved.

Published May 14, 2026