Electrical Formulas

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

η_m = P_out × 746 / P_in

where

η_m = efficiency
P_out = shaft power out (horsepower, hp)
P_in = 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

η_m = P_out / P_in

where

η_m = motor efficiency
P_out = shaft power out (watts, W)
P_in = 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

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

T_N = ln(2) x C x R₂
T_N = 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
T_P = positive or high time from each pulse
T_N = negative or low time from each pulse

Temperature Conversions

T_°F = Degrees Fahrenheit (°F)
T_°C = Degrees Celsius (°C)
T_K = 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)

T_K = (T_°F + 459.67) × 5/9

Degrees Celsius (°C) to Kelvins (K)

T_K = T_°C + 273.15

Kelvins (K) to Degrees Fahrenheit (°F)

T_°F = T_K × 9/5 − 459.67

Kelvins (K) to Degrees Celsius (°C)

T_°C = T_K − 273.15

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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

SI Units

 

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

 

 

Notes

 

References

[BIPM] Bureau International des Poids et Mesures [International Bureau of Weights and Measures]. “The International System of Units (SI), 8th Edition”. PDF. 2006. ISBN 92-822-2213-6. Accessed August 14, 2017. Link goes to English language version.

[THOM] Thompson, Ambler; Taylor, Barry N. “Guide for the Use of the International System of Units (SI) (Special Publication 811)”. PDF. 2008. Gaithersburg, MD: National Institute of Standards and Technology. Accessed February 14, 2018.

[WIKI1] Wikipedia contributors. “List of Mathematical Symbols”. Wikipedia. February 10, 2018. Accessed February 14, 2018.