If you need number density and you already have density, molar mass and number of free electrons, this calculator does the substitution for you. It suits a quick check, a homework answer you want to confirm, or any figure you need to sanity test.
What Is the Number Density Calculator?
This number density calculator is for the kind of problem where you know the physical quantities but not the number you need. It turns density, molar mass and number of free electrons into number density.
Physics calculations go wrong in predictable ways, usually through mixing units or dropping a digit. Work through the result one step at a time and check that the figures are the size you would expect at each stage.
How the Number Density Physics Works
The relationship is applied step by step, and each step is a standard piece of physics rather than a single opaque formula. That means you can check the intermediate values against what the theory predicts, which is usually faster than checking only the final answer.
Keep every value in the same unit system throughout the calculation. Mixing metres and feet part way through is the single most common reason a correct formula gives a wrong answer.
Units, Assumptions and the Limits of the Model
The calculation assumes ideal conditions: no air resistance, no heat loss, and dimensions that do not change while you work. Those assumptions are reasonable for most classroom and engineering estimates, and unreasonable for anything more precise.
Where a value is a rate, it has to be quoted for the same period as everything else. A per-hour figure cannot be combined with a per-day figure without converting one of them first.
A Worked Example
Working through an example, with density set to 10, molar mass set to 5, number of free electrons set to 2, the calculator returns number density of 0.24089. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out number density?
Enter density, molar mass and number of free electrons. The calculator then works through the relationship and reports number density.
What does the number density actually calculate?
It takes density, molar mass and number of free electrons and converts them into number density using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter density?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.