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 |
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√ (P × R) | result in volts V | |||||||
Current I = |
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result in amperes A | |||||||
Resistance R = |
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result in ohms Ω | |||||||
Power P = | V × I | R × I 2 |
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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
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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 | |
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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 |
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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 |
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bar[BIPM] | bar | pressure | 1 bar = 0.1 MPa 1 bar = 100 kPa 1 bar = 105 Pa |
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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 |
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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 |
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hectare[BIPM] | ha | area | 1 ha = 1 hm2 1 ha = 104 m2 |
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hour[BIPM] | h | time | 1 h = 60 min 1 h = 3600 s |
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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 |
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maxwell[BIPM] | Mx | magnetic flux | 1 Mx = 1 G cm2 1 Mx = 10−8 Wb |
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millimetre of mercury[BIPM] | mmHg | pressure | 1 mmHg ≈ 133.322 Pa | |
minute[BIPM] | ′ | plane angle | 1′ = (1/60)° 1′ = (π/ 10 800) rad |
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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 |
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poise[BIPM] | P | dynamic viscosity | 1 P = 1 dyn s cm−2 1 P = 0.1 Pa s |
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second[BIPM] | ″ | plane angle | 1″ = (1/60)′ 1″ = (π/ 648 000) rad |
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stilb[BIPM] | sb | luminance | 1 sb = 1 cd cm−2 1 sb = 104 cd m−2 |
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stokes[BIPM] | St | kinematic viscosity | 1 St = 1 cm2 s−1 1 St = 10−4 m2 s−1 |
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tonne[BIPM] | t | mass | 1 t = 103 kg |
Formula Symbols
Formula Symbol | It Measures | SI Unit | SI Unit Symbol | Notes | |||||||
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B |
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tesla = weber per square metre |
T |
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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 |
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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.