Basic Electrical and Structural Engineering Formulas Explained
Ohm's Law, resistor networks, and beam deflection explained with the underlying physics and real numbers.
Whether you're wiring a small electronics project or sizing a structural beam, a handful of foundational formulas cover the majority of everyday engineering questions.
Ohm's Law: the three-way relationship
Voltage, current, and resistance are locked together by V = I × R. Push 2 amps of current through a 10-ohm resistor and you get V = 2 × 10 = 20 volts across it. Rearranging the same formula (I = V/R or R = V/I) lets you solve for whichever variable you don't already know — you only ever need two of the three values to find the third.
Power follows directly from this: P = I²R (or equivalently P = VI). That 2-amp, 10-ohm example dissipates P = 2² × 10 = 40 watts as heat, which is exactly why resistor power ratings matter — a resistor rated for less than the power it's dissipating will overheat and fail.
Series vs. parallel resistance
Resistors in series simply add: R_total = R1 + R2. Resistors in parallel combine by reciprocal: R_total = (R1×R2)/(R1+R2) for two resistors. A 100Ω and 220Ω resistor in series give 320Ω total; in parallel, they give (100×220)/(320) ≈ 68.75Ω — always less than the smallest individual resistor, because adding a parallel path always gives current an easier way through.
Voltage dividers
A voltage divider splits an input voltage across two series resistors, with the output measured at their junction: Vout = Vin × R2/(R1+R2). A 12V supply across a 1kΩ and 2kΩ resistor pair gives Vout = 12 × 2000/3000 = 8V at the junction — a simple, passive way to scale a voltage down without active components.
Beam deflection: how much a structure bends
For a simply supported beam with a center point load, maximum deflection is δ = PL³/(48EI), where E is the material's elastic modulus and I is the beam's moment of inertia. Doubling the span length (L) increases deflection by a factor of 2³ = 8 — which is why beam length matters so much more than most other variables in structural deflection, and why longer spans need disproportionately stiffer beams.
Where to calculate your own numbers
- The Ohm's Law calculator and power calculator cover voltage/current/resistance/power relationships
- The resistor series & parallel calculator and voltage divider calculator handle multi-resistor circuits
- The beam deflection calculators (point load and uniform load) estimate structural bending for a given span and load