Core physics and chemistry formulas, each with a worked example that was recomputed in code and matches the calculators. Use SI units (kg, m, s, mol, K, Pa) unless a row says otherwise, and note that temperature in the gas law must be in kelvin: K = °C + 273.15.
Formulas
| Quantity | Formula | Example |
|---|---|---|
| Density | ρ = m / V |
54 g in 20 cm³ (aluminium): 2.70 g/cm³ |
| Weight (a force) from mass | W = m × g, g = 9.80665 m/s² |
70 kg: 686.5 N (weight is a force, mass is not) |
| Moles from mass | n = mass / molar mass |
10 g of NaCl (58.44 g/mol): 0.1711 mol |
| Molarity | M = moles / litres |
0.1711 mol in 0.5 L: 0.342 M |
| Molecular weight | sum of atomic weights |
H₂O = 2 × 1.008 + 15.999 = 18.015 |
| Dilution | C₁V₁ = C₂V₂ |
2 M × 50 mL = C₂ × 200 mL gives C₂ = 0.5 M |
| Ideal gas law | PV = nRT, R = 8.314462618 J/(mol·K) |
1 mol at 273.15 K and 101,325 Pa: 22.41 L |
| Projectile range on level ground | R = v² × sin(2θ) / g |
20 m/s at 45°: 40.79 m (45° gives the longest range) |
| Radioactive half-life | N = N₀ × (½)^(t / T) |
80 g, half-life 5 days, after 15 days: 10 g |
Try them
The Density Calculator, Mass Calculator and Weight Calculator cover the first rows, while the Molarity Calculator, Molecular Weight Calculator and Dilution Calculator handle solutions. The Ideal Gas Law Calculator solves for any one of P, V, n and T, and the Projectile Motion Calculator gives range, height and flight time. For decay see the Half-Life Calculator; for circuits see the Electrical Formulas Cheat Sheet.
Common mistakes
- Celsius in the gas law. Always convert to kelvin first.
- Mass versus weight. Your mass is the same on the Moon; your weight there is about a sixth.
- Volume in the wrong unit. Molarity needs litres, not millilitres.