# Electrical Formulas

Contents

## The 12 Basic Formulas

There are 12 basic formulas that are used regularly. The formulas are for calculating voltage, current, resistance, and power. With any two values you can calculate the other two.

Voltage V  = I × R
 P I
(P × R) result in volts V
Current I  =
 V R
 P V
 √ P R
result in amperes A
Resistance R  =
 V I
 P I 2
 V 2 P
result in ohms Ω
Power P  = V × I R × I 2
 V 2 R
result in watts W

## Formulas

### Energy Lost in a Resistor

TODO: Find the actual formulas for this.

A 12 V battery is connected in series with a resistance of 50 ohm. The power consumed in the resistor can be calculated as

P = (12 V)2 / (50 ohm)

= 2.9 W

### Electrical Motor Efficiency when Shaft Output is measured in Horsepower

If power output is measured in horsepower (hp), efficiency can be expressed as

ηm = Pout × 746 / Pin

where

ηm = efficiency
Pout = shaft power out (horsepower, hp)
Pin = electric power in to the motor (Watt, W)

### Electrical Motor Efficiency when Shaft Output is measured in Watts

If power output is measured in watts (W), efficiency can be expressed as

ηm = Pout / Pin

where

ηm = motor efficiency
Pout = shaft power out (watts, W)
Pin = electric power in to the motor (watts, W)

### Conductance

G = 1 / R
G = I / V

where

G = siemens (S)
R = resistance (Ω)
I =  electric current through the object
V = voltage (electrical potential difference) across the object

### IC 555 Timer Formulas

f = 1 / [ ln(2) x C x (R1 + 2R2) ]
f = 1.44 / C x (R1 + 2R2) … where … 1 / ln(2) = 1.44

TP = ln(2) x C x (R1 x R2)
TP = 0.693 x C x (R1 x R2) … where … ln(2) = 0.693

TN = ln(2) x C x R2
TN = 0.693 x C x R2 … where … ln(2) = 0.693

where

C = value of capacitor in farads
R1 and R2 = value of the input resistance
f = frequency in kHZ
TP = positive or high time from each pulse
TN = negative or low time from each pulse

### Temperature Conversions

T°F = Degrees Fahrenheit (°F)
T°C = Degrees Celsius (°C)
TK = Kelvins (K)

Degrees Fahrenheit (°F) to Degrees Celsius (°C)

T°C = (T°F − 32) × 5/9
T°C = (T°F − 32) / (9/5)
T°C = (T°F − 32) / 1.8

Degrees Celsius (°C) to Degrees Fahrenheit (°F)

T°F = T°C × 9/5 + 32
T°F = T°C × 1.8 + 32

Degrees Fahrenheit (°F) to Kelvins (K)

TK = (T°F + 459.67) × 5/9

Degrees Celsius (°C) to Kelvins (K)

TK = T°C + 273.15

Kelvins (K) to Degrees Fahrenheit (°F)

T°F = TK × 9/5 − 459.67

Kelvins (K) to Degrees Celsius (°C)

T°C = TK − 273.15

## International System of Units (SI) Units

### SI Prefixes

Prefixes are added to unit names to produce multiples and sub-multiples of the original unit, All multiples are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand.

Prefix Symbol Value
yocto– y 10−24 = 0.000 000 000 000 000 000 000 001
zepto– z 10−21 = 0.000 000 000 000 000 000 001
atto– a 10−18 = 0.000 000 000 000 000 001
femto– f 10−15 = 0.000 000 000 000 001
pico– p 10−12 = 0.000 000 000 001
nano– n 10−9 = 0.000 000 001
micro– µ 10−6 = 0.000 001
milli– m 10−3 = 0.001
centi– c 10−2 = 0.01
deci– d 10−1 = 0.1
100 = 1
deca– da 101 = 10
hecto– h 102 = 100
kilo– k 103 = 1 000
mega– M 106 = 1 000 000
giga– G 109 = 1 000 000 000
tera– T 1012 = 1 000 000 000 000
peta– P 1015 = 1 000 000 000 000 000
exa– E 1018 = 1 000 000 000 000 000 000
zetta– Z 1021 = 1 000 000 000 000 000 000 000
yotta Y 1024 = 1 000 000 000 000 000 000 000 000

### Common Non-SI Units

The SI is capable of describing most useful and measurable physical quantities, but many non-SI units still appear in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture. The Comité International des Poids et Mesures (International Committee for Weights and Measures) recognized and acknowledged such traditions by compiling a list of non-SI units accepted for use with SI. The units that are defined in BIPM are marked [BIPM].

Unit Symbol Measures Definition Notes
ångström[BIPM] Å length 1 Å = 10−10 m
1 Å = 10−8 cm
1 Å = 10−4 μm
1 Å = 0.1 nm
1 Å = 100 pm
bar[BIPM] bar pressure 1 bar = 0.1 MPa
1 bar = 100 kPa
1 bar = 105 Pa
barn[BIPM] b area 1 b = 100 fm2
1 b = (10−12 cm)2
1 b = 10−28 m2
The barn is a unit of area employed to express cross sections in nuclear physics.
bel B logarithmic ratio quantities
day[BIPM] d time 1 d = 24 h
1d = 86 400 s
decibel dB logarithmic ratio quantities 1 dB = 0.1 B
degree[BIPM] ° plane angle 1° = (π/180) rad
dyne[BIPM] dyn force 1 dyn = 10−5 N
erg[BIPM] erg energy 1 erg = 10−7 J
gal[BIPM] Gal acceleration 1 Gal = 1 cm s−2
1 Gal = 10−2 m s−2
The gal is a special unit of acceleration employed in geodesy and geophysics to express acceleration due to gravity.
gauss[BIPM] G magnetic flux density 1 G = 1 Mx cm−2
1 G = 10−4 T
hectare[BIPM] ha area 1 ha = 1 hm2
1 ha = 104 m2
hour[BIPM] h time 1 h = 60 min
1 h = 3600 s
knot[BIPM] kn speed 1 kn = (1852/3600) m/s
litre[BIPM] L, l volume 1 L = 1 l
= 1 dm3
= 103 cm3
= 10−3 m3
maxwell[BIPM] Mx magnetic flux 1 Mx = 1 G cm2
1 Mx = 10−8 Wb
millimetre of mercury[BIPM] mmHg pressure 1 mmHg ≈ 133.322 Pa
minute[BIPM] plane angle 1′ = (1/60)°
1′ = (π/ 10 800) rad
minute[BIPM] min time 1 min = 60 s
nautical mile[BIPM] M distance 1 M = 1852 m
neper Np logarithmic ratio quantities
œrsted[BIPM] Oe magnetic field 1 Oe ≜ (103 / 4π) A m−1 The symbol ≜ means “is defined as” or “is equal by definition to”.[WIKI1]
phot[BIPM] ph illuminance 1 ph = 1 cd sr cm−2
1 ph = 104 lx
poise[BIPM] P dynamic viscosity 1 P = 1 dyn s cm−2
1 P = 0.1 Pa s
second[BIPM] plane angle 1″ = (1/60)′
1″ = (π/ 648 000) rad
stilb[BIPM] sb luminance 1 sb = 1 cd cm−2
1 sb = 104 cd m−2
stokes[BIPM] St kinematic viscosity 1 St = 1 cm2 s−1
1 St = 10−4 m2 s−1
tonne[BIPM] t mass 1 t = 103 kg

## Formula Symbols

Formula Symbol It Measures SI Unit SI Unit Symbol Notes
B
• magnetic field
• magnetic flux density
• induction
tesla = weber per
square metre
T
 T = Wb = V · s m 2 m 2
C electric capacitance farad F F = C/V = A·s/V = s/Ω
D electric flux density coulomb per square meter C/m 2
E electric field strength volt per meter V/m
EV illuminance and
luminous emittance
lux Ix Ix = Im/m 2
G electric conductance siemens S S = 1/Ω
H magnetic field strength ampere per meter A/m
I electric current ampere A
IV luminous intensity candela cd
J current density ampere per square meter A/m 2
L inductance henry H H = Wb/A = V·s/A = Ω·s
LV luminance candela per square meter cd/m 2
P power watt, joule per second,
newtonmeter per second
W, J/s, Nm/s P = W / t
Q electric charge coulomb C amperesecond A·s = C
R electric resistance DC ohm Ω Ω = V/A
T period second s T=1 / f
T temperature Kelvin K 0 K = −273,15 °C
V electric voltage,
electric potential difference
volt V V = W/A
W work W = energy E wattsecond, Joule,
newtonmeter
Ws, J, Nm W = P × t
Z electric impedance AC ohm Ω Ω = V/A
Θ magnetomotive force ampere-turn A upper-case theta U+0398
Φ magnetic flux weber Wb voltsecond V·s = Wb

upper-case phi U+03A6

ΦV luminous flux lumen Im upper-case phi U+03A6
ρ electrical resistivity ohm times meter or
ohm times square millimeter
divided by meter
Ω · m
Ω · mm 2/m
lower-case rho U+03C1