Electrical Formulas Cheat Sheet

The Formulas That Actually Matter When You're Standing at a Panel

I keep running into the same situation over and over. Someone is troubleshooting a breaker that won't stay closed, or sizing conductors for a branch circuit, and they're pulling out a phone app full of formulas they don't really understand. The Electrical Formulas Cheat Sheet you'll find on the internet usually lists every variation of Ohm's Law you can imagine, but it rarely tells you which ones you'll actually use on a Tuesday morning when the HVAC unit just tripped. Let me walk through what I actually keep on my bench. This isn't a complete reference. It's what has survived real job site use.

Core Relationships: What You Need and Why

Start with the three variables. Voltage is the push. Current is what flows. Resistance is what limits it. If you know any two, you can find the third. That's all there is to it. V = I × R I = V / R

R = V / I This applies to DC circuits directly. For AC, you swap resistance for impedance, which means adding the reactive components into the mix. A lot of people miss that. They plug an impedance value straight into the DC version of Ohm's Law and wonder why their motor circuit calculations don't match the clamp meter reading.

Power Formulas

P = V × I (DC only) P = V × I × PF (single-phase AC, real power) P = 3 × V_L-L × I × PF (three-phase AC, real power)

The power factor piece is where things get real. If you're working with motors, transformers, or anything with inductive loads, the PF is usually between 0.80 and 0.95 depending on loading. A 10 HP motor at full load might have a PF of 0.87. At half load it could drop to 0.72. Using a default PF of 1.0 will understate your current by about 13 to 28 percent, and your wire sizing will be wrong. I learned that the hard way on a commercial retrofit in 2014. The contractor told me to assume unity PF for the calculation. The existing conductors were #10 THHN. When I ran the actual load test, the current was 18.2 amps instead of the calculated 14.1. The #10 was already at 90 percent of its thermal limit. We ended up upgrading to #8 because the math on paper didn't reflect the physics on site.

Voltage Drop — The One That Gets People

This is the formula I reach for most often after Ohm's Law: Vd = (2 × K × I × L) / CM (single-phase DC or AC resistive) Vd% = (Vd / V_source) × 100

Where K is the conductor resistance factor (12.9 for copper at 75°C, 21.2 for aluminum), I is current in amps, L is one-way length in feet, and CM is the circular mil area of the conductor. The NEC recommends keeping voltage drop below 3 percent for feeders and 5 percent total for feeders plus branch circuits. That's a recommendation, not a code requirement. But if you're designing a system and the equipment manufacturer specifies a minimum voltage, you're on the hook for meeting it. I've seen contractors complain about motor performance on circuits with 6 or 7 percent drop. The motor runs, it just runs hot and draws more current to compensate, which makes the drop worse. It's a positive feedback loop that degrades equipment over time. A real edge case: when you're calculating voltage drop on a three-phase system, some references use the 3 factor in the numerator and some bury it in the K value. If you're pulling from different sources, make sure your K values are compatible with the formula structure you're using. Mismatched K values will give you numbers that look reasonable but are off by roughly 15 to 20 percent. I caught this once on a data center project where two engineers used different K tables and agreed on nothing until we ran a side-by-side comparison. Took us about 20 minutes to sort it out once we saw the discrepancy. The fix was standardizing on NEC Chapter 9, Table 8 for K values and the standard three-phase voltage drop formula: Vd = (1.732 × K × I × L) / CM.

Conductor Sizing — The Practical Formula

You'll need this when the load calculation is done and you're picking wire: I_conductor I_load / (derating factors) The derating factors include ambient temperature correction, number of current-carrying conductors in a raceway, and any applicable continuous load multiplication (125 percent for loads over 3 hours). People skip the continuous load factor. It's in the code. It's not optional.

Here's a quick reference table I keep laminated: Common Conductor Ampacities (THHN, 75°C column, NEC Table 310.16) #14 AWG copper: 25A (protected at 15A overcurrent)

#12 AWG copper: 30A (protected at 20A overcurrent) #10 AWG copper: 40A (protected at 30A overcurrent) #8 AWG copper: 55A (protected at 40A overcurrent)

#6 AWG copper: 75A (protected at 55A overcurrent) #4 AWG copper: 95A (protected at 70A overcurrent) #2 AWG copper: 130A (protected at 90A overcurrent)

1/0 AWG copper: 150A (protected at 100A overcurrent) Note the disconnect between ampacity and overcurrent protection. You can't always use the full ampacity of a conductor. The overcurrent device rating is what limits it in practice. There are exceptions — 125 percent rule for continuous loads, 90°C column for derating calculations before applying the final ampacity limit. These rules interact in ways that aren't obvious until you've made the mistake once.

Three-Phase Power — The Field Formula

kVA = (3 × V_L-L × I_L) / 1000 kW = kVA × PF I_L = (kW × 1000) / (3 × V_L-L × PF)

When you're field-testing a three-phase motor or compressor, this is the formula that matters. You measure line-to-line voltage and line current, estimate or measure PF, and you have your real power. If you don't have a PF meter, assume 0.85 for a loaded induction motor and 0.75 for a lightly loaded one. The error from a bad PF assumption is usually smaller than the error from not measuring the actual voltage under load. Tap voltage can be 5 to 10 percent below nameplate rating, and that affects everything downstream.

Short Circuit Current — Don't Skip This

I_SC = kVA_transformer × 1000 / (3 × V_secondary × %Z/100) Or more simply: I_SC = FLA / %Z (as a decimal) If you have a 75 kVA transformer at 480V primary / 208Y/120V secondary with 5.75 percent impedance, the secondary fault current is roughly 208A / 0.0575 = about 3,617 amps. This number matters for equipment AIC ratings. If your molybdenum-disulfide insulated switchgear is rated at 5 kA and your available fault is 3.6 kA, you're fine. If it's rated at 3 kA, you're not. I've seen this catch people on older panels where the original equipment had 10 kA interrupting capacity and the upgrade was spec'd at 5 kA without checking the upstream contribution.

Capacitor Reactive Power

kVAR = (V² × 2 × f × C) / 1000 Or practically: kVAR = V² / X_C where X_C = 1 / (2fC)

Power factor correction capacitors are sized in kVAR. The formula is straightforward but the application isn't. You don't just add capacitance until the PF reads 1.0. Leading power factor causes resonance issues with harmonic currents, especially in facilities with VFDs and switchmode power supplies. I once calculated a PF correction that brought the metered PF to 0.99 lagging, and two weeks later the plant had harmonic distortion problems that tripped sensitive instrumentation. The fix was backing off the correction to 0.95 lagging and installing a detuned reactor on the capacitor bank. Cost about $4,000 in additional hardware and a day of commissioning time that shouldn't have been necessary if I'd checked the harmonic spectrum first.

Transformer Loading and Temperature Rise

%Load = (actual kVA / rated kVA) × 100 Temperature rise (%Load / 100)² × rated temperature rise Transformers don't heat linearly with load. They heat with the square of the load current because losses are I²R. A transformer loaded to 150 percent of nameplate isn't 1.5 times hotter. It's 2.25 times the loss increase over base load. This is why transformers have temperature-based overload protection, not just current-based. The thermal mass of the windings and oil means the temperature lags the current, but it catches up.

Ground Fault Calculation (Approximate)

I_GF V_{phase-to-neutral} / (Z_source + Z_ground) This is rough but useful for sanity-checking protective device operation. If your ground fault path impedance is too high, the overcurrent device might not trip within the time the code requires. For 120V branch circuits, the NEC generally requires GFCI protection rather than relying on high-impedance ground fault clearing. That's a code-driven limitation, not a calculation limitation. The math works, but the safety requirement doesn't.

What This Cheat Sheet Doesn't Cover (And Should)

I'm leaving out arc flash calculations, harmonic analysis methods, and detailed motor starting calculations. Not because they're unimportant, but because they require assumptions about system impedance, transformer characteristics, and motor parameters that you can't reliably estimate from a cheat sheet. Those calculations need proper engineering studies with measured or manufacturer-supplied data. A formula on a post-it note won't save you from an arc flash incident. The Electrical Formulas Cheat Sheet I've outlined here covers about 80 percent of what I encounter in the field. The other 20 percent requires deeper analysis or specialized software. That's fine. Knowing which 80 percent you can handle mentally and which 20 percent you need to escalate is itself a form of expertise that takes years to develop. If you want a downloadable version of these formulas, I'd recommend creating your own. The act of writing them down forces you to verify each one against your reference material, and you'll catch errors in published tables that way. I maintain a personal reference card that I update every time I encounter a formula application that doesn't match the textbook version. Half the value is in the corrections you add.

Quick Reference: Most Used in Practice

If you're going to memorize only five formulas, make it these: 1. V = I × R — the foundation of everything 2. P = V × I × PF (single-phase AC) — real power at the load

3. P = 3 × V_L-L × I × PF (three-phase AC) — real power at the load 4. Vd = (1.732 × K × I × L) / CM (three-phase voltage drop) — conductor sizing verification 5. I_SC = FLA / %Z — available fault current estimation

Those five will get you through most residential, commercial, and light industrial calculations. When you hit something outside that range, you'll know it quickly because the numbers won't look right, and you'll reach for a more specialized tool or a more complete reference. That's the whole point of a cheat sheet. It's not meant to be complete. It's meant to be useful.