A unit conversion re-expresses one quantity in a different unit without changing the quantity itself. Pick a category, type a value, then choose the units to convert from and to; the ladder below draws every unit in that category on one logarithmic scale so you can see how big the factor between them really is.
Unit Conversions
Pick a quantity, type a value, then choose the units to go from and to. Every scale conversion is one multiplication, result = value × factor; the ladder shows how big that factor really is. Temperature is the exception, and it gets its own picture.
What Is the Unit Conversions Simulator?
The unit conversions simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Set any value, pick from and to units across force, energy, pressure, length and temperature, and see the factor. It reports Result value × factor as you drag the sliders.
| Quantity reported | Example value |
|---|---|
| Result value × factor | 101325 Pa |
Reading a Conversion as a Distance, Not a String of Digits
The five buttons across the top of the panel — Force, Energy, Pressure, Length and Temperature — do more than filter a list. Each one loads its own table of units together with the SI base unit they are all measured against, so the ladder is drawn in newtons, joules, pascals or metres depending on what you picked. Choose a category, type a value, then pick a unit on the From row and one on the To row. Both light up as ticks on the ladder, with a bracket drawn between them carrying the factor that separates them.
That bracket is why the lab draws a picture at all. Written down, an electronvolt is 1.602176634 × 10-19 joules — a string of characters that carries no sense of size whatsoever. Placed on a logarithmic ladder it becomes a distance: the eV tick sits about twenty-five decades below the kilowatt-hour tick, and that gap is something you can actually look at. A second lane underneath marks where your own quantity falls once it is expressed in the base unit, so the number you typed is placed among the units rather than floating free of them.
For every category but one the sim is performing a single sum, result = value × factor_from ÷ factor_to. Each factor is nothing more than how many base units one of that unit is worth, so a conversion means stepping out to the base unit and then back in again. Many of those factors are exact by definition rather than measured, which is why some answers come out perfectly clean — a fuller tour of where the defined values come from is in the guide to physics unit conversions, and the base units themselves are covered in SI units of measurement in physics.
Temperature is the exception, and pressing its button changes the picture deliberately. There is no factor that turns Celsius into Fahrenheit, because the two scales do not share a zero — doubling a Celsius reading does not double the Fahrenheit one, and treating temperature as though it multiplies is the commonest mistake in this topic. Select Temperature and the ladder gives way to three scales side by side with one line ruled across all three: the same physical point, three different numbers. To shift a prefix rather than cross unit systems, the SI prefix converter does that in one step.
Frequently asked questions
Which conversions are exact?
Most of them, because these units are defined rather than measured. The inch is exactly 0.0254 metres by the 1959 international agreement, which makes the foot, the yard and the mile exact too, so 1 mile converts to exactly 5280 feet with nothing left over. The standard atmosphere is defined as exactly 101325 pascals and the torr as exactly one 760th of it, so 1 atm is exactly 760 torr. The calorie is exactly 4.184 joules, and the electronvolt has been exactly 1.602176634 × 10^-19 joules since the 2019 SI redefinition fixed the elementary charge. Only a few, such as the pound-force and the psi, are irrational multiples written out to the last digit the arithmetic can hold.
Why does temperature behave differently in the sim?
Because temperature scales are affine rather than proportional. Kelvin, Celsius and Fahrenheit put their zeros in three different places, so converting between them needs a shift as well as a stretch, and no single multiplying factor can do the job. Selecting Temperature therefore replaces the magnitude ladder with three scales drawn side by side and one line running across all of them: a single physical temperature reading as three different numbers. Behind that picture the sim converts your input to kelvin first and then back out to the unit you asked for, and it refuses any input below absolute zero, because 0 K is a floor rather than a convention.
How do I convert eV to joules here?
Select Energy, type 1 into the value box, then choose eV as the from unit and J as the to unit. The reading is 1.602176634 × 10^-19 J, and the bracket drawn across the ladder carries that same figure as the factor separating the two ticks. Because the factor is exact by definition, you can enter any number of electronvolts and the answer keeps the full defined value rather than a rounded copy of it.
Why does cm³ to m³ move by a million?
Because a volume is a length cubed. One centimetre is a hundredth of a metre, so a cubic centimetre is a hundredth cubed of a cubic metre, which is one millionth of it. The prefix moves two decades on a length but six on a volume, and that is the step most often dropped. This lab converts lengths rather than volumes, so use the length ladder to see the two-decade gap from cm to m, then cube it yourself for the volume.
Does the sim round?
The arithmetic runs at full double precision and only the display is rounded, to ten significant figures. That is wide enough to show a defined factor in full, so 1 atm reads 101325 rather than a truncated version, while still hiding the residue floating-point arithmetic leaves behind: 1 foot converts to 12 inches, not 12.000000000000002. Readings below 0.0001 or at ten million and above switch to exponential form. Converting a value out to another unit and straight back returns what you started with.
References & formula source
- BIPM — The International System of Units (SI Brochure), 9th edition (2019): the defining constants, base units and coherent derived units.
- B. N. Taylor & A. Thompson (eds.) — NIST Special Publication 811, "Guide for the Use of the International System of Units (SI)", Appendix B: factors for units accepted for use with the SI.
- National Bureau of Standards — "Refinement of Values for the Yard and the Pound" (1959): the international yard and pound agreement fixing the inch at exactly 0.0254 m.
- Further reading: Conversion of units — Wikipedia