These four formulas cover the basics of mechanics, electricity, and chemistry — each one is simple once you see it, but each has a specific units mistake that trips people up. Here's each formula with a worked example and the trap to watch for.
Density: mass per unit volume
Worked example: an object with a mass of 500g and a volume of 200cm³:
| Calculation | Result |
|---|---|
| 500 g ÷ 200 cm³ | 2.5 g/cm³ |
| Converted to SI units | 2,500 kg/m³ |
Common mistake: mixing g/cm³ and kg/m³ without converting — they're not numerically interchangeable. To go from g/cm³ to kg/m³, multiply by 1,000 (since 1 g/cm³ = 1,000 kg/m³). Density is also how "does it float" gets determined — an object with a density lower than the fluid it's placed in will float, which is why oil (roughly 0.92 g/cm³) floats on water (1.0 g/cm³).
Force: Newton's second law
Worked example: a 10kg object accelerating at 3 m/s²:
| Calculation | Result |
|---|---|
| 10 kg × 3 m/s² | 30 N (newtons) |
Common mistake: confusing mass and weight. Mass (kg) is how much matter an object contains and stays constant anywhere; weight is the force of gravity acting on that mass (weight = mass × gravitational acceleration, roughly 9.8 m/s² on Earth) and changes depending on location — the same 10kg mass weighs less on the Moon because the Moon's gravity is weaker, even though its mass hasn't changed.
Ohm's law: the relationship between voltage, current, and resistance
Worked example: a circuit with 12V across it and 2A of current flowing:
| Measure | Calculation | Result |
|---|---|---|
| Resistance | 12V ÷ 2A | 6 Ω (ohms) |
| Power | 12V × 2A | 24 W (watts) |
Common mistake: forgetting that Ohm's law only directly relates voltage, current, and resistance — power is a separate (though related) calculation that many people conflate with resistance since both involve multiplying or dividing the same two inputs.
Molarity: concentration of a solution
Worked example: 2 moles of a solute dissolved to make 0.5 liters of solution:
| Calculation | Result |
|---|---|
| 2 mol ÷ 0.5 L | 4 mol/L (also written as 4 M) |
Common mistake: using the volume of solvent added instead of the total volume of the finished solution. If you dissolve a solute in some solvent and the resulting solution's total volume isn't exactly the volume of solvent you started with (which is common, especially with solids dissolving), molarity should be calculated from the final solution volume, not the starting solvent volume.
Common mistakes across all four
- Mixing unit systems without converting. Grams vs. kilograms, centimeters vs. meters — always convert to a single consistent system before calculating.
- Confusing mass with weight, or resistance with power. These pairs are related but not interchangeable, and using the wrong one changes both the units and the meaning of the result.
- Using the wrong volume for molarity — total solution volume, not solvent volume added.
- Forgetting units in the final answer. A bare number (30, 6, 2,500) is meaningless without stating whether it's newtons, ohms, or kg/m³.
Try the calculators
Each formula above has a dedicated calculator: the density calculator, force calculator, Ohm's law calculator, and molarity calculator.
Frequently asked questions
What is the formula for density?
Density = Mass ÷ Volume. The SI unit is kilograms per cubic meter (kg/m³), though grams per cubic centimeter (g/cm³) is common for smaller everyday objects.
What is Newton's second law of motion?
Force = Mass × Acceleration (F = ma). Force is measured in newtons, mass in kilograms, and acceleration in meters per second squared.
What is Ohm's law?
Ohm's law states that Voltage = Current × Resistance (V = IR). Rearranged, Resistance = Voltage ÷ Current, which is how a resistance value is calculated from a measured voltage and current.
What is molarity and how is it calculated?
Molarity is a measure of solution concentration, calculated as moles of solute divided by liters of solution (mol/L, also written as M). It tells you how concentrated a solution is, independent of the total volume prepared.