Physics Unit Conversions

Unit conversion is a change of scale, not a change of quantity: the source and target units describe the same physical dimension. The reliable workflow is to write the original value, multiply by a clearly labelled conversion factor, and confirm with dimensional analysis that the units cancel to leave the target unit. Convert before substituting into an equation so you never mix scales inside a formula for force, energy, pressure, or fields.

How to check a physics conversion

Start by identifying the dimension involved: length, mass, time, energy, pressure, charge, field strength, or temperature. Then use a conversion factor equal to one, such as 1000 m / 1 km or 1 eV / 1.602176634 x 10^-19 J. Write the factor so the original unit cancels. If the unwanted unit does not cancel algebraically, the factor is upside down.

For example, converting 72 km/h to m/s uses two factors: 72 km/h x 1000 m / 1 km x 1 h / 3600 s = 20 m/s. The number changes because the scale changes, but the physical speed is the same. This same unit-cancellation method works for pressure, work, impulse, power, electric potential, and wave quantities.

Common conversions in physics problems

• Speed: km/h to m/s by dividing by 3.6; m/s to km/h by multiplying by 3.6.
• Energy: electronvolts to joules using 1 eV = 1.602176634 x 10^-19 J.
• Pressure: atmospheres, bar, pascals, torr, and psi should be converted to pascals before using SI formulas.
• Mass: grams and metric tons should usually be converted to kilograms before force, momentum, or energy calculations.
• Length: centimeters, millimeters, astronomical units, and light-years should be converted before gravitational or wave equations.
• Temperature: Celsius differences and Kelvin differences have the same size, but absolute thermodynamic formulas require kelvin.

Conversion mistakes to avoid

Do not round too early in a multi-step calculation; keep extra significant figures until the final answer. Be careful with squared or cubed units: converting cm^2 to m^2 requires squaring the length factor, and converting cm^3 to m^3 requires cubing it. Also distinguish mass from weight. Kilograms measure mass, while newtons measure force, so changing kilograms into newtons requires a gravitational field value such as g = 9.81 m/s^2 near Earth's surface.

When a problem combines several quantities, convert every input to a consistent unit system before calculating. A spring constant in N/cm, a distance in millimeters, and an energy answer in joules can all be correct individually, but mixing them directly in E = 1/2 kx^2 gives the wrong result. The safest habit is to list the known values, rewrite each one in SI units, solve the equation, and then convert the final answer into the unit requested by the question.

Interactive converter

Convert across length, mass, energy, force, pressure, temperature, speed, power, angle, and frequency. Type a value and the tool shows both the converted result and the conversion factor it used, so you can check the dimensional reasoning.

Related tools and references

• Physics calculators — worked numerical solvers with full derivations.
• Formula library — equations with variable definitions and units.
• Physics glossary — concise definitions of key quantities and units.
• All topics — the full curated directory of the site.