# Formula Tables

### Electrical Formulas for Calculating Amperes, Horsepower, Kilowatts, & kVA

Find: Direct Current Alternating Current
kW E * I / 1000 E * I * PF / 1000 E * I * PF * 1.732 / 1000
kVA E * I / 1000 E * I * 1.732 / 1000
hp E * I * %Eff / 746 E * I * %Eff * PF / 746 E * I * %Eff * PF * 1.732 / 746
Percent Efficiency (%Eff) = (Output ÷ Input) * 1000

Power Factor (PF) = true power ÷ apparent power = kW ÷ kVA

Power Factor = Ratio of True to Apparent Power = W ÷ VA

Power Factor Percent = (kW ÷ kVA) * 100

Note: Direct Current formulas do not use PF nor 1.732 (√3) and 1Ø formulas do not use 1.732 (√3)

## NEC Tables_Cheat Sheet

TableDescriptionPageNotes
110.28Enclosures70-50
220.54Demand Factors-Dryers70-73
220.55Demand Factors-Cooking Appliances70.74"most confusing NEC table"
Annex Cconductors of the same size70-713
01Raceway Conductor Fill70-679
04Raceway Trade Size70-680Pipe Fill
05Conductor Area, Insulated70-684
05AConductor Area, Insulated, Compact70-688
08Conductor Area, Bare70-689
250.102(C)(1)Alt-Cur Systems Grounded, Main Bonding, System Bonding, & Supply-side Bonding Jumper Conductors70-119
250.122Minimum Size Equipment Grounding Conductors for Grounding Raceway & Equipment70-125
250.66Grounding Electrode Conductor, Alt-Cur Systems70-116
310.104(A)Conductor Insulation Properties70-166
310.15(B)(2)(a)Ampacity Correction Factors
310.15(B)(16)Conductor Ampacity70-150
314.16(A)Metal Outlet Box Conductor Limits70-176only used with conductors of the same size
314.16(B)Volume Allowance required per Conductor
430-72(B)Motor Over-Current Device Maximum Rating70-311
430.248Full-Load Currents, 1Ø, Alt-Cur Motors
430.250Full-Load Currents, 3Ø, Alt-Cur Motors
430.37Motor Minimum Allowed Overload Units70-306
430.52Motor Short-Circuit & ╧-Fault Devices Maximum Rating70-308
450.3(B)Transformer Over-Current %70-333

# Formulas

### Formula Table

Description Qualifier Formula Notes Shorthand

## Miscellaneous

√3 = 1.732
208 * 1.732 = 360
240 * 1.732 = 415
440 * 1.732 = 762
480 * 1.732 = 831
VCuFt = L x W x D Volume

Electrical Power Cost (\$)

= True Power (W) consumed per month * Cost per kWh

## Series and Parallel Circuits

Rt Series Circuit Rt = R1 + R+ R3 + etc.
Parallel Circuit Rt = 1 resistor Ω / number of resistors equal resistance
Rt = (R1 x R2) / (R1 + R2) only 2 resistors
Rt = 1/[(1/R1) + (1/R2) + (1/R3)…] Preferred method

## Direct & Alternating Current

VA

= W / PF Apparent Power (VA)
= kW / PF
= E*I

W

= VA * PF True Power (W)
= E*I Direct Current (DC)
= E * I * PF Alternating Current (AC)

PF

= W / VA Power Factor
= kW / kVA

Eff

= Output W / Input W Efficiency / CIRCLE Output Watts / EFF * Input Watts
Input W = Output W / Eff
Output W = Eff * Input W

PV

= Effective Value / 0.707 AC Peak Value
= Effective Value * 1.414

EV

= RMS Value AC Effective Value
= PV * 0.707
= PV / 1.414

VRMS

= VPeak *0.7 Root Mean Square

VPeak

= VRMS*1.4

XC

= 1/(2 * π * f * C) Capacitive Reactance

XL

= 2 * Pi * f * L Inductive Reactance

## Motor Formulas

Horsepower (HP) = 746 W 1 HP = 746W, Motor Output
= Output W / 746
Full Load Amps (FLA) = FLA = 746W x HP / E x Eff x PF 1 Ø
= FLA = 746W x HP / E x Eff x PF X 1.732 3 Ø
Running Current I = E / Z
Z = √R2 + XL
VA = E*FLC 1 Ø VA Calculations, Motor Input
= E*FLC*1.732 3 Ø VA Calculations, Motor Input
η = 0.7457 x hp x Load / Pi Efficiency
Load = Pi x η / hp x 0.7457

## Transformer Formulas

Primary : Secondary Turns Ratio
I = I = VA/E 1 Ø, Determine Line Current
= I = VA/(E * 1.732) 3 Ø, Determine (Primary) Line Current
Primary Current = Txfr VA Rating ÷ Primary Voltage 1 Ø Pri-I =TxfrVA / Pri-E
Primary Current =  Txfr VA Rating ÷ (Primary Voltage * 1.732) 3 Ø, also:  ‘Primary Phase Power / (Primary Phase Volts * 1.732)’ Pri-I =TxfrVA / (Pri-E*√3)
Primary Protection = Primary Current * Table 450.3(B) % 1Ø & 3Ø, NEC-2017-pg 70-333 Pri-OC = Pri-I * 450.3% & PriOC= Pri-I* 450.3%
Secondary Current = Txfr VA Rating ÷ (secondary Voltage * 1.732) 3 Ø
Secondary Conductor Ampacity = Primary Protection Ampacity * (Primary Voltage / Secondary Voltage)
High-leg Voltage = Line Voltage * 1.732
High-leg Voltage = (Line Voltage ÷ 2)* 1.732
Short Circuit Current

## Conductor Formulas

DC Conductor Ω = (Conductor Ω / 1000′) * Conductor Length
AC Conductor Ω = (Conductor ohms-to-neutral Ω / 1000′) * Conductor Length
Area = πr2 3.14 x (Dia. x ½)2
Corrected Amps = Table 310.15(B)(16) amps * Ambient Temp. Correction Factor table 310.15(B)(2)(a)
Adjusted Amps = Table 310.15(B)(16) amps * Bundled amp Adjustment Factor table 310.15(B)(3)(a)
Adjusted & Corrected Ampacity = Table 310.15(B)(16) amps * Temperature factor * Bundled adjustment factor
INeutral = √(ILine12 + ILine22) – (ILine1 * ILine2) Unbalanced 3-wire Wye Secondary Neutral Current; Square-root over entire equation (MH-pg263)
In = L1 – L2 Neutral Current in 3 wire, 1Ø circuit
In = √(L12 + L22 + L32) – [(L1 x L2) + (L2 x L3) + (L1 x L3)] SqRt of entire equation, Neutral Current in 3 wire, 3Ø circuit

## Raceway and Box Calculation Formulas

Raceway fill Limitation Ratio = Raceway Diameter / Conductor Diameter
Raceway Sizing = Conductor Cross-Sectional Area Ch9, Tbl 8 or 9
= Conductors Total Cross-Sectional area
= Raceway % Fill Ch9, Tbl 1 or 4

## Commercial Calculation Formulas

Receptacle number permitted per circuit = Circuit VA rating / 180 VA for each yoke General-Use Receptacles 220.44
Demand Load per Line = Connected Load per Line * Demand Factor Commercial, Marinas
I = VA / E Commercial, Manufactured Home Parks, Recreational Vehicle Parks
I = VA / (E * 1.732) New Restaurant Feeder/Service Load Optional Method Calculation
Demand Load = VA * Number of Sites * Demand Factor Commercial, Manufactured Home Parks
Demand Load = Primary Rating * Multiplier (Table 630.11(A)) Arc Welder, Supply Conductor Ampacity, Single
Demand Load = Primary Rating * Multiplier (Table 630.11(A)) * Welder % (630.11(B) Arc Welder, Supply Conductor Ampacity, Group
Demand Load = Primary Rating * Multiplier (Table 630.31(A)(2)) Resistance Welder, Supply Conductor Ampacity, Single
Demand Load = Primary Rating * Multiplier (Table 630.31(A)(2)) * Welder % (630.31(B) Resistance Welder, Supply Conductor Ampacity, Group

## Dwelling Unit Formulas

Demand Load = Connected Load * Demand Factor Dwelling Unit, Standard Method, Appliances
Demand Load = Column C Value * Multiplier Dwelling Unit, Standard Method, Cooking equipment
Demand Load = Connected Load * Table 220.55 Demand Factor Multi-dwelling Unit, Standard Method, Cooking equipment
Total Demand Load = Connected Load * Table 220.84 Demand Factor Multi-dwelling Unit, Optional Method
Service Size = Demand Load VA / System Volts Multi-dwelling Unit, Standard & Optional Method, Feeder & Service Conductor Sizing, 1 Ø
Service Size = Demand Load VA / (System Volts * 1.732) Multi-dwelling Unit, Standard Method, Feeder & Service Conductor Sizing, 3 Ø
Service Demand Load = Connected Load * Table 220.54 Demand Factor Multi-dwelling Unit, Neutral Load
Neutral Amperes = Neutral Demand Load / System Voltage Dwelling Unit, Neutral Load
Neutral Demand Load = Service Demand Load * 70% Multi-dwelling Unit, Neutral Load
Air-Conditioning VA = E * I Multi-dwelling Unit, Standard Method, Air-conditioning

## Voltage Drop Calculation Formulas

VD(E) = I*R 1Ø, Circuit conductor Voltage Drop
Cmils =  (2*K*I*D)/VD Sizing Conductors
= (1.732*K*I*D)/VD
VD(E) =  (2*K*I*D)/Cmils Determine Conductor Voltage Drop
= (1.732*K*I*D)/Cmils
D = (Cmils*VD)/(2*K*I) Determining Maximum Conductor Limiting Voltage Drop
= (Cmils*VD)/(1.732*K*I)
I = (Cmils*VD)/(2*K*D) Limit Current to Limit Voltage Drop / Determining the Maximum Load
= (Cmils*VD)/(1.732*K*D)

## Formula Legend

E Voltage
I Current / Amperage
R Resistance
P Power
W Watts
PF Power Factor
Z Impedance
VD Voltage Drop of the circuit in volts
K 12.9Ω=Cu, 21.2Ω=Alum; ‘DC Constant’ approximation; Constant k represents the DC Ω for a 1000 Cmils conductor at a 1000′ length operating at 75°C; “True K” (or actual) conductor value calculated by conductor Cmil area * conductor Ω  per foot; ‘K’ constant suitable for AC current circuits where conductors do not exceed 1/0.
I Amperes load at 100% (not 125%)
L Inductance / henrys
D Distance load is from the power supply; Use the length of one conductor to the load (not 2)
CM or Cmils = Circular Mils; circular mil area of a conductor listed in NEC-Ch9-Tbl8
η Efficiency as operated in %
Por Nameplate rated horsepower
Load Output power as a % of rated power
Pi 3Ø power in kW
hp Nameplate rated HP
XC Ω
XL
π 3.14
f frequency / hertz
c capacitance / farads
Rt Total circuit resistance, Sum of all resistors
Es Power Supply Voltage
Q

AC adjustment required for circuit conductors 2/0 & larger (skin) effects of self-induction.

AC Ω (NEC-Ch9-Tbl9) ÷ DC Ω (NEC-Ch9-Tbl8)

kVA volt-ampere, the notation for which is VA, is a measure of apparent power and uses watts for units.

## Formula Chart Notes

Know how to determine current on the neutral of a 3Ø system
Know how to determine resistance & capacitance on series & parallel circuits
3 important formulas: 1) I=E/R, 2) P=IE, 3) I=(E*√3)/R