Everyday Physical Science Calculations Explained
Density, half-life, and pH explained with the formulas and real-world examples like carbon dating.
A surprising number of science-class formulas turn out to be genuinely useful outside the classroom — for cooking, dating archaeological finds, or just understanding a lab report.
Density: why some things float
Density is simply mass divided by volume: ρ = m/V. An object with a density lower than the fluid it's placed in floats; higher, it sinks. A 500g object occupying 250cm³ has a density of 500/250 = 2 g/cm³ — twice the density of water (1 g/cm³), so it would sink in water but might float in a denser liquid like mercury.
Half-life and carbon dating
Radioactive decay follows N(t) = N₀ × (1/2)^(t / half-life), where N₀ is the starting quantity and t is elapsed time. Carbon-14 has a half-life of about 5,730 years. Starting with 100g and waiting 11,460 years (exactly two half-lives) leaves 100 × (0.5)^(11460/5730) = 100 × 0.5² = 25g — a quarter of the original amount, because two full half-life periods have passed. This exact formula is the basis of carbon dating: measuring how much carbon-14 remains in an organic sample reveals roughly how long ago the organism died.
pH: a logarithmic scale, not a linear one
pH measures hydrogen ion concentration using pH = −log₁₀[H⁺]. Because it's a logarithmic (base-10) scale, each whole-number step represents a 10x change in acidity — a pH of 4 is ten times more acidic than a pH of 5, not just "one unit" more. A hydrogen ion concentration of 0.0001 mol/L works out to pH = −log₁₀(0.0001) = 4, solidly in the acidic range (below 7).
Wavelength and frequency
Any wave — light, sound, radio — follows f = v/λ, where v is the wave's propagation speed. Visible light travels at roughly 299,792,458 m/s; a wavelength of 500 nanometers (green light) corresponds to a frequency of 299,792,458 / 0.0000005 ≈ 599.6 terahertz. The same formula works for sound waves too, just swap in the speed of sound (~343 m/s in air) instead of the speed of light.
Calculate your own
- The density calculator works for any mass/volume pair
- The half-life calculator models decay for any substance and any elapsed time
- The pH calculator and wavelength/frequency calculator cover the other two formulas above directly