Unit Conversion Formulas, Factors, and Offsets
Understand base-unit conversion formulas, scale factors, temperature offsets, reverse conversions, significant digits, and rounding with examples.
How do the Unit Converter formulas work?
This formula page defines the variables used by the Unit Converter, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.
Formula Overview
The converter sends the entered value to a shared base unit, then converts that base value to the requested destination unit. This two-stage method keeps direct and reverse conversions consistent across every supported category.
Variable Definitions
| Variable | Meaning |
|---|---|
| x | Entered source value |
| sfrom | Source unit scale relative to the category base unit |
| ofrom | Source unit offset |
| sto | Destination unit scale relative to the base unit |
| oto | Destination unit offset |
General Base-Unit Formula
Base value = x × sfrom + ofrom
Converted value = (base value - oto) ÷ sto
For proportional units, both offsets are zero. The relationship then simplifies to converted value = x × sfrom ÷ sto.
Temperature Formulas
| Conversion | Formula |
|---|---|
| Celsius to Fahrenheit | °F = °C × 9/5 + 32 |
| Fahrenheit to Celsius | °C = (°F - 32) × 5/9 |
| Celsius to Kelvin | K = °C + 273.15 |
| Kelvin to Celsius | °C = K - 273.15 |
The added or subtracted constant is why temperature cannot be handled by a scale factor alone.
Exact Conversion Factors
| Relationship | Factor |
|---|---|
| 1 inch | 0.0254 meter |
| 1 foot | 0.3048 meter |
| 1 pound | 0.45359237 kilogram |
| 1 US gallon | 3.785411784 liters |
| 1 UK gallon | 4.54609 liters |
| 1 standard atmosphere | 101,325 pascals |
Reverse Conversion
If one source unit equals f destination units, one destination unit equals 1 ÷ f source units. The calculator reports this reciprocal relationship as a quick independent check.
Worked Calculation: 10 Kilograms to Pounds
- Use kilogram as the mass base unit, so the base value is 10.
- One pound equals 0.45359237 kilogram.
- Calculate 10 ÷ 0.45359237.
- The unrounded result is approximately 22.046226 pounds.
- Displayed to three decimals, 10 kilograms = 22.046 pounds.
Rounding Policy
Decimal.js retains additional calculation precision. Displayed results use the selected two or three decimal places. Values too small or large for a readable fixed decimal use scientific notation so digits are not clipped.
Formula Assumptions
- Both units belong to the same measurement category.
- Configured unit factors use the stated definitions.
- Temperature inputs must not fall below absolute zero.
- Rounding changes the display, not the underlying conversion.
- Measurement uncertainty and instrument tolerances are outside the formula.
Try the Formula
Use the Unit Converter to inspect its calculation steps or open the worked unit conversion examples.