Sources & formulas

Every calculator on WaterHeaterCalcs rests on established water-heating thermodynamics plus stable water-heater conventions. Unlike topics with a time dependency, “verification” here is mathematical: each formula is tested against known values and is therefore correct for good. Here are the technical foundations by area.

Identities & thermodynamics

  • Heat energy: BTU = gallons × 8.33 lb/gallon × ΔT (°F); ΔT = output temp − inlet temp.
  • Recovery rate: gph = input BTU/hr × recovery efficiency ÷ (8.33 × ΔT); electric input BTU/hr = kW × 3412.
  • Reheat time: hours = gallons × 8.33 × ΔT ÷ (input BTU/hr × efficiency).
  • First-Hour Rating: FHR ≈ 0.70 × storage gallons + recovery gph.
  • Peak-hour demand: Σ(uses × DOE gallons-per-use); tankless GPM = Σ simultaneous fixture flow.
  • Annual energy: kWh = daily gallons × 365 × 8.33 × ΔT ÷ 3412 ÷ UEF; therms = … ÷ 100000 ÷ UEF; propane gallons = … ÷ 91500 ÷ UEF.
  • Expansion tank: Vt = Ve ÷ (1 − supply psi ÷ relief psi), Ve ≈ 0.02 × tank gallons.
  • Cost: (unit/parts + labor + add-ons − discount) ×(1 + contingency).

Convention typicals (labeled)

  • DOE hot-water use per fixture: shower ~20 gal, bath ~20, shave ~2, hand/face ~4, dishwasher ~6, clothes washer ~7 — labeled, measure your routine.
  • Fixture flow GPM: shower ~2.0, kitchen faucet ~1.5 — labeled.
  • Gallons + First-Hour Rating by household: 1–2 people ~30–40 gal (FHR 40–55), 3–4 ~50–60 (FHR 60–75), 5+ ~60–80 — labeled, confirm the EnergyGuide label.
  • Typical UEF by type: electric tank ~0.92, gas tank ~0.62, gas tankless ~0.90, heat pump ~3.5 — labeled.
  • Lifespan by type: gas tank ~8–12 yr, electric tank ~10–15, tankless ~18–20, heat pump ~10–15 — labeled.
  • Inlet water temperature by region, cost bands, labor multipliers, contingency ~10%: labeled planning typicals.
  • 120 °F setting: the common recommended temperature (the scald vs Legionella tradeoff) — a manufacturer and professional matter, not medical advice here.

Cost & energy tools

  • Every cost tool uses the prices you enter (unit $, parts $, labor $, add-on $) and every energy tool your own $/kWh and $/therm — no equipment, labor or utility rate is stored, so the site needs no maintenance. Cost bands are a labeled sanity guide.
  • Quote check: the tools compare your quoted total against a labeled band for the type — a sanity flag, not a bid.

Equipment, labor and utility prices, product data-sheet values (UEF, First-Hour Rating, GPM) and local rules vary by place and change over time — always confirm your unit’s rated First-Hour Rating, GPM and UEF on its EnergyGuide label, follow the manufacturer’s instructions and local code, round sizing up and leave peak headroom, defer gas, venting, combustion, the temperature-&-pressure relief valve, the scald / Legionella tradeoff and code compliance to a licensed professional, and get itemized written quotes from a licensed, insured plumber before you commit.