The 12 Numbers Every Engineering Intern Should Memorize (and the Sanity Checks They Unlock)

Senior engineers catch wrong answers in seconds because they carry a dozen anchors in their head. Here they are — g, ρ of water, 1 bar, 1 hp, room temperature in three units, the speed of sound and more — with the one-line sanity check each one enables.

The difference between an intern and a senior engineer in a design review is rarely knowledge of theory. It is that the senior engineer looks at "pump power: 4.7 MW" and says that can't be right before anyone opens a spreadsheet. That reflex is built from a small set of memorised anchors. Here are twelve, each with the sanity check it unlocks.

Mechanics

1. g ≈ 9.81 m/s² ≈ 32.2 ft/s²

Check: anything in free fall gains ~10 m/s every second. A 1 kg mass weighs ~10 N. A 100 kg person weighs ~1 kN. If a force on a human-scale object comes out in MN, look again.

2. Density of water: 1,000 kg/m³ = 1 g/cm³ = 62.4 lb/ft³

Check: a cubic metre of water is a tonne. A 10 m × 5 m × 2 m tank holds 100 tonnes. Steel is ~7.85×, aluminium ~2.7×, air ~1/800 of water (1.2 kg/m³).

3. 1 bar ≈ 1 atm ≈ 100 kPa ≈ 14.5 psi ≈ 10 m of water

Check: every 10 m of depth adds 1 bar. A 30-storey building's water riser needs ~10 bar at the base. Car tyres run 2–2.5 bar; a bicycle 5–8 bar; a scuba tank 200 bar.

4. 1 MPa = 1 N/mm²

Check: mild steel yields at ~250 MPa, so a 10 mm × 10 mm bar (100 mm²) carries ~25 kN before yielding — about 2.5 tonnes. Concrete: 20–50 MPa in compression, ~10% of that in tension.

Energy and power

5. 1 kWh = 3.6 MJ; 1 hp ≈ 0.75 kW; 1 kW ≈ 1.34 hp

Check: a kettle is 2–3 kW. A car engine 100–300 kW. A human sustains ~100 W (~0.13 hp), sprints at ~1 kW. If a bicycle "needs 5 kW", the units are wrong.

6. Specific heat of water: 4.18 kJ/(kg·K); latent heat of vaporisation ≈ 2,260 kJ/kg

Check: heating 1 L of water by 80 K takes ~335 kJ ≈ 0.093 kWh — a 2 kW kettle does it in under 3 minutes. Boiling it off takes 7× more energy than heating it to 100 °C.

7. Lower heating value of fuels: gasoline ≈ 44 MJ/kg (≈ 32 MJ/L), natural gas ≈ 50 MJ/kg, coal ≈ 25 MJ/kg, lithium-ion battery ≈ 0.7 MJ/kg

Check: a 50 L tank holds 1.6 GJ ≈ 440 kWh of chemical energy; at 30% engine efficiency that is ~130 kWh at the wheels — comparable to a large EV battery. Explains why EV batteries weigh 400–600 kg.

Thermal and fluids

8. Room temperature: 20 °C = 68 °F = 293 K. Body: 37 °C = 98.6 °F = 310 K

Check: any thermodynamic calculation with T in °C instead of K gives garbage — an ideal-gas result at "20" instead of "293" is off by 15×. If an absolute temperature is below 200 K or above 2,000 K in ordinary equipment, check the units.

9. Speed of sound: ~343 m/s in air (20 °C), ~1,480 m/s in water, ~5,000 m/s in steel

Check: lightning 3 s after the flash = 1 km away. A pipe 100 m long rings at ~25 Hz in steel (v/2L). Subsonic aircraft cruise at ~250 m/s (Mach 0.8).

10. Kinematic viscosity: water ≈ 1×10⁻⁶ m²/s, air ≈ 1.5×10⁻⁵ m²/s

Check: Re = vD/ν. Water at 1 m/s in a 50 mm pipe → Re ≈ 50,000 → turbulent. Almost all practical pipe flows are turbulent; a "laminar" answer for a water main is a warning sign.

Electrical

11. Household voltage and the 1 kW ↔ 4–8 A rule

Check: at 230 V, 1 kW draws ~4.3 A; at 120 V, ~8.3 A. A 15 A US circuit tops out at ~1.8 kW, which is why American kettles are slow. A 32 A EV charger at 230 V single-phase is ~7 kW.

12. Speed of light ≈ 3×10⁸ m/s ≈ 30 cm/ns; e ≈ 1.6×10⁻¹⁹ C; k_BT at room temp ≈ 25 meV

Check: a signal crosses a 30 cm PCB trace in ~1.5 ns (slower than c in FR4) — at 1 GHz that is 1.5 clock cycles, so timing matters. 25 meV is why silicon diodes conduct at ~0.6–0.7 V and why thermal noise is what it is.

The habit that makes them useful

Before you compute anything, write a one-line estimate using only these anchors and powers of ten. Then compute. If the two disagree by more than 3×, one of them is wrong and it is usually the detailed one — a slipped unit, a squared factor, a °C where a K belonged. This takes 20 seconds and catches the errors that reach production.

Next in this series: the ten unit mistakes that actually ship — from lbm/lbf to kW/kWh — and the one-line habit that prevents each.