Physics vs Statistics: Which Formula Before You Type Numbers

Physics homework and stats homework both say “calculator” and then destroy a lab report. V = IR is not P = VI. ½mv² is not v = v₀ + at. A z-score is not a t-test. This hub is the combined physics-stats silo on pancalc: mechanics and circuits first, then the inferential toolkit. Education only — not a PE stamp, not medical statistics, not “this p-value publishes.”

If you only remember one sentence: state the unit of the answer (volt, watt, m/s, joule, dimensionless Re, dB, σ, p-value) before picking a page.

Circuits: Ohm then power

Ohm’s law is V = IR for the lumped resistor teaching model. Series and parallel networks are extra algebra. Temperature-dependent R is extra physics.

Electrical power is P = VI in the same simple model. A 12 V / 2 Ω resistor dissipates 72 W only if that current actually flows and the part can throw that heat. Household AC, power factor, and three-phase are not this identity.

Do not use photon energy to size a heater.

Motion and energy

Velocity, acceleration, time is the SUVAT family under constant a. v = v₀ + at, s = v₀t + ½at², v² = v₀² + 2as. Variable acceleration needs calculus (math numerical integration is not a substitute for a dynamics course).

Kinetic and potential energy tracks ½mv² and m g h (near-Earth teaching g). Energy conservation problems still need you to state the zero of potential. A kinematics time does not equal a joule.

kg to newton is W = m g. Mass is not force. Bathroom scales that say “kg” are a social convention; the newton page is the SI teaching correction.

Hooke’s law and impulse bundles F = kx (ideal spring) and J = FΔt = Δp (impulse-momentum, constant force teaching). A spring problem is not an impulse problem until a collision appears. Mixing k with Reynolds is a lab-report genre known as “I had numbers.”

Fluids, waves, sound

Reynolds number estimates laminar vs turbulent tendency in a stated geometry. Critical Re is an order-of-magnitude tradition, not a certificate.

Density and water weight is m = ρV and often weight in newtons. Pool volume × 1000 kg/m³ is a mass; do not call it Re.

Frequency and wavelength is v = fλ with v = c in vacuum for light, slower in a medium for sound. Guitar strings are a different v.

Photon energy and wavelength is E = hc/λ (or E = hf). A green photon’s eV is not a household kilowatt-hour (ecology electricity CO₂ is a different silo) and not Ohm’s law.

Decibel distance attenuation sketches spreading (and sometimes absorption) in a simple model: +6 dB when you halve distance from a point source in the classroom story. Rooms have reflections; OSHA and concert limits are policy. This is not a medical hearing test.

Statistics: describe, then infer

Standard deviation measures spread. Population vs sample (n vs n−1) matters. SD is not a standard error (that divides by √n) and not a z-score.

Z-score is (x − μ) / σ when you state μ and σ. A z of 2 is “two SDs above the mean” in that model. It is not a p-value until you name a tail and a distribution.

T-test compares means with sample variance. Assumptions (independence, roughly normal-ish at small n, equal variance options) are the course, not a hidden checkbox that makes a journal.

One-way ANOVA extends the mean comparison to several groups. A significant F does not tell you which pair differs (post-hoc is extra). Two groups: prefer the t-test page unless your lab protocol standardized on ANOVA software.

Poisson is counts in time/space with rate λ. Radioactive teaching counts, call-center sketches. Not a binomial with n trials and p — unless n is large, p small, np = λ, which is an approximation, not an identity swap.

Binomial and chi-square covers binary trials and χ² goodness-of-fit / independence teaching. Chi-square is not ANOVA. Binomial n, k, p is not a z-score unless you use a normal approximation on purpose.

Sample size and power asks how large n should be for a stated effect, α, and power. It is a planning identity. It does not rescue a fishing expedition after you already p-hacked.

Permutation and combination is nPr vs nCr (order matters or not). A password counting argument can start here; generating a password is the household generator, not this formula.

Random number generator draws from a uniform (or stated) teaching RNG. Simulation, assigning treatments, bingo-like classroom demos. Not cryptographic secrets (password generator / entropy pages). Not a t-test.

Worked collisions between the two halves

A lab measures current through a resistor (Ohm, power) and reports three trial means with SD. Those are two sentences. Do not compute Re on the resistor unless you are actually in a flow lab.

A kinematics cart + photogate: use v, a, t. If the question is “how much KE at the bottom,” then energy. If the question is “are three track setups different,” then ANOVA or t-tests on the times — after you state that times are the response.

Photon E = hc/λ does not belong in a decibel problem. Both mention “wave” in casual speech. One is a quantum teaching energy; one is log intensity.

Constants, logs, and sample size honesty

g ≈ 9.81 m/s² vs 10 m/s² changes newtons and mgh by ~2%. State g. c = 2.998×10⁸ m/s in vacuum; in glass you need n. k in F = kx is N/m, not Reynolds’s dimensionless 1. Impulse 10 N for 0.5 s is 5 N·s, equal to Δp; if mass 2 kg, Δv = 2.5 m/s — kinematics after the collision, energy only if you know whether the collision is elastic.

Sound: −6 dB per distance doubling is spherical spreading in the myth; a line source is closer to −3 dB. Photon: 500 nm is about 2.48 eV teaching (E(eV) ≈ 1240/λ(nm)). That eV is not a household kWh.

Statistics walkthrough: list 2, 4, 4, 4, 5, 5, 7, 9. Mean 5, sample SD 2 (the famous textbook set). z of the value 9 is (9−5)/2 = 2 if you treat those as μ,σ — which they are not if they are a sample. A two-sample t-test needs two lists, not one z. ANOVA on three labs with n = 3 each is legal as arithmetic and weak as inference. Poisson λ = 3, P(X=0) = e⁻³ ≈ 0.050. Binomial n = 10, p = 0.5, P(X=10) = 1/1024. Combinations C(10,2) = 45; permutations P(10,2) = 90. Sample size for a tiny effect at 90% power can exceed your grant — the calculator is allowed to say a large n; you are allowed to redesign the effect.

Random numbers: assigning 20 rats to two treatments with a teaching RNG is fine; generating a server password is not. nPr does not mint the password either.

If your physics lab’s last question is “is the difference significant?”, you have left SUVAT. If your stats lab’s last question is “what is the current?”, you have left p-values.

Lab period, two subjects

Physics bench: a 9 V battery, 330 Ω resistor. Ohm: I = 9/330 ≈ 0.027 A. Power: P = I²R ≈ 0.25 W. If the resistor is in water flowing in a 1 cm tube, Reynolds is a different experiment with ρ, v, L, μ. If you weigh 0.250 kg on a string, newtons are about 2.45 N; that is not the resistor power. A cart from rest at 2 m/s² for 3 s: v = 6 m/s, s = 9 m. KE of 0.5 kg at 6 m/s is 9 J. A spring k = 200 N/m compressed 4 cm: F = 8 N, energy ½kx² = 0.16 J if you leave Ohm. A 440 Hz tone in air at 343 m/s: λ ≈ 0.78 m. A 532 nm photon: E ≈ 2.33 eV. A point-source teaching drop from 2 m to 4 m: −6 dB in the cartoon.

Stats bench on the same afternoon: 30 reaction times, mean and SD first. One student 2 SD slow is a z, not a diagnosis. Two labs of n = 12: t-test on means. Three firmware versions: ANOVA. Counts of radioactive clicks per 10 s with mean 4: Poisson. Coin 20 flips: binomial. Dice fairness: χ². How many mice for 80% power at a 0.5 SD effect: sample size page — if n = 64 and you have 12 mice, change the design. Seating 5 of 12 students in a row: P(12,5). Committee of 5: C(12,5). Assign IDs with the teaching RNG.

The failure mode is one spreadsheet with I, p, and Re in adjacent columns untitled. Title the columns with units.

What this hub will not do

It will not stamp a pressure vessel, certify a hearing map, or publish your p-value. It will not choose a one-tailed vs two-tailed test for your career. It will not know whether your course uses σₙ or σₙ₋₁. It will not replace a circuit simulator with parasitics. It will not integrate variable acceleration just because the kinematics page has a t field.

What it will do is keep watts next to volts only when you mean power, keep joules off the SUVAT line unless you converted mass and velocity on purpose, and keep Poisson counts out of ANOVA tables. Teachers can assign “use the Ohm page then the SD page on three trials” as two sentences. That is a good session; untitled columns are not.

Search fragments: “energy calculator” might mean mechanical ½mv², electrical P=VI, photon hc/λ, or even food calories (health silo). “Wave calculator” might mean fλ or decibels or photons. “Distribution calculator” might mean z, t, Poisson, or binomial. This article is the disambiguation layer so the related-widget in the same category does not have to do all the work. When two fragments fit, open the tool whose output unit matches the blank on the worksheet, then the other. Neighbor hubs: ecology wind turbines are not Reynolds; household decimal hours are not kinematics t; percent-math is not a z-score; lab half-life is first-order chemistry, not a Poisson waiting time unless the course says so. If the blank is in volts, you are still on Ohm even if the lab also asks for an SD.

Practical takeaway

Physics: pick the conserved or constitutive story (charge/Ohm, energy, momentum/impulse, continuum Re, waves). Statistics: describe with SD, locate with z, compare means with t or ANOVA, model counts with Poisson or binomial, plan n with power, count arrangements with nPr/nCr, simulate with the RNG. If the number is a calendar date or a molarity, leave this hub.