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Constants / Conversions

CONSTANTS

Decimal Multiplier Prefixes
Multiplier	Power	Prefix	Symbol
	10¹⁰⁰			googol
1,000,000,000,000	10¹²	tera	T	trillion
1,000,000,000	10⁹	giga	G	billion
1,000,000	10⁶	mega	M	million
1,000	10³	kilo	k	thousand
100	10²	hecto	h
10	10¹	deka	da
0.1	10^-1	deci	d
0.01	10^-2	centi	c
0.001	10^-3	milli	m
0.000 001	10^-6	micro	µ
0.000 000 001	10^-9	nano	n
0.000 000 000 001	10^-12	pico	p
0.000 000 000 000 001	10^-15	femto	f
0.000 000 000 000 000 001	10^-18	atto	a

In the U.S. sometimes g's or a grand refers to a thousand (10³).
In some (European) countries 10¹⁸ is a trillion, and 10¹² is a billion.

Speed of Light (c) in a Vacuum
299,792,456.2	meters / second
983,571,050.5	feet / second
1,079,252,842	kilometers / hour
670 616 625.4	miles / hour
582,749,914.9	nautical miles / hour
299,792.4562	kilometers / second
186,282.3959	miles / second
161,874.9763	nautical miles / second
983.571 050 5	feet / microsecond
0.983 571 051	feet / nanosecond

Approximate Speed of Sound (Mach 1)
Sea Level	Linear decrease to	36,000 to 82,000 feet	Linear Increase to	82k to 154k feet
765 mph	Linear decrease to	660 mph	Linear Increase to	755 mph

Speed of Sound at Sea Level = 1 mile / 4.7 second.
Speed of Sound from 36k - 82k ft = 1 mile / 5.5 seconds.

Other Constants
Permittivity of free space:	e_o	=	µ_o^-1 c^-2	Farads/meter
	e_o	=	8.854 185 x 10^-12	F/m

Permeability of free space:	µ_o	=	4(pi) x 10^-7	Henrys/meter
	µ_o	=	1.26 637 061 x 10^-6	H/m

Intrinsic Impedance of free space:	Z_o	=	376.73	ohms

Acceleration due to Gravity:	g	=	9.80 665	m/s²
	g	=	g 32.1740	ft/s²

Boltzmann's Constant:	k	=	1.380 622 x 10^-23	Watt*sec/°K

Transcendental Numbers

PI (π)
π = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510...

π radians
1 radian

= 180°
= 180°/π = 57.3°

Base of Natural Logarithms (ln)
e = 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69995...

Logarithm Conversions
Natural (ln) to / from Base 10 (log)

log (x)	= ln (x) / ln (10) = 0.434 294 4819 ln (x)
ln (x)	= log₁₀ (x) / log ₁₀ (e) = 2.302 585 093 log (x)

U.S. Interstate
Left Shoulder	Lane Width	Right Shoulder	Height Clearance	Maximum Grade
3 ft	12 ft	10 ft	14 ft	5% city 6% mountains

Standard Railroad Gauge: 4 feet, 8.5 inches

CONVERSIONS

SPEED
	Exact	Approximate
1 meter / second =	1 / 0.3048	3.28	feet / second
	3.6	3.6	kilometers / hour
	1 / 0.44704	2.24	miles / hour
	900 / 463	1.94	nautical miles / hour

1 foot / second =	0.3048	0.3	meters / second
	1.09728	1.1	kilometers / hour
	15 / 22	0.68	miles / hour
	274.32 / 463	0.59	nautical miles / hour

1 kilometer / hour =	1 / 3.6	0.28	meters / second
	5 / 5.4864	0.91	feet / second
	1 / 1.609344	0.62	miles / hour
	1 / 1.852	0.54	nautical miles / hour

1 mile / hour =	0.44704	0.45	meters / second
	22 / 15	1.47	feet / second
	1.609344	1.61	kilometers / hour
	402.336/463	0.87	nautical miles / hour

1 nautical mile / hour = 1 knot =	463 / 900	0.51	meters / second
	463/274.32	1.69	feet / second
	1.852	1.85	kph
	463 / 402.336	1.15	miles / hour

DISTANCE
	Exact	Approximate
1 inch =	0.0254	0.03	meters

1 foot =	12	12	inches
	1/ 3	0.33	yards
	0.3048	0.30	meters

1 yard =	36	36	inches
	3	3	feet
	0.9144	0.91	meters

1 meter =	1 / 0.0254	39.37	inch
	1 / 0.3048	3.28	feet
	1 / 0.9144	1.09	yards

1 kilometer =	1 / 1.852	0.54	nautical miles
	1 / 1.609344	0.62	miles
	1 / 0.0009144	1093.6	yards
	1 / 0.0003048	3280.8	feet
	1000	1000	meters

1 mile (statute) =	1609.344 / 1852	0.87	nautical miles
	1.609344	1.6	kilometer
	1760	1760	yards
	5280	5280	feet
	1609.344	1609	meters

1 nautical mile =	1852 / 1609.344	1.15	miles
	1.852	1.852	kilometers
	1852 / 0.9144	2025.4	yards
	1852 / 0.3048	6076.1	feet
	1852	1852	meters

1 nautical mile (UK) =	1853.184	1853.1	meters

ACCELERATION
	Exact		Approximate

1 m / s² =	1 / 0.3048	=	3.2808	ft / s²
	9 / 2.5	=	3.6	kph / s
	1 / 0.44704	=	2.2369	mph / s
	900 / 463	=	1.9438	knots / s
	1 / 9.80665	=	0.1020	g's

1 ft / s² =	0.3048	=	0.3048	m / s²
	15 / 22	=	0.6818	mph / s
	1.09728	=	1.0973	kph / s
	274.32 / 463	=	0.5925	knots / s
	0.3048 / 9.80665	=	0.0311	g's

1 mph / s =	22 / 15	=	1.4667	ft / s²
	0.44704	=	0.447	m / s²
	1.609344	=	1.6093	kph / s
	402.336 / 463	=	0.8690	knots / s
	0.44704 / 9.80665	=	0.0456	g's

1 kph / s =	2.5 / 9	=	0.2778	m / s²
	5 / 5.4864	=	0.9113	ft / s²
	1 / 1.609344	=	0.6214	mph / s
	1 / 1.852	=	0.54	knots / s
	2.5 / (9 * 9.80665)	=	0.0283	g's

1 knot / s =	463 / 900	=	0.5144	m / s²
	463 / 274.32	=	1.6878	ft / s²
	463 / 402.336	=	1.1508	mph / s
	1.852	=	1.852	kph / s
	463 / (900 * 9.80665)	=	0.0525	g's

1 g =	9.80665	=	9.81	m / s²
	9.80665 / 0.3048	=	32.1740	ft / s²
	9.80665 [ 3600 / (5280 * 0.3048)]	=	21.9369	mph / s
	3.6 * 9.80665	=	35.3039	kph / s
	3600 * 9.80665 / 1852	=	19.0626	knots / s

1 g = 9.80665 m/s² by International Definition

ft/s²
m/s²
mph/s
kph/s
knots/s

= feet per second per second
= meters per second per second
= miles per hour per second
= kilometers per hour per second
= nautical miles per hour per second

Decibels
ratio	=	10^dB/10
dB	=	10 log(ratio)

3 dB
-3 dB

≈
≈

2
0.5

Power Decibels
mW	=	10^dBm/10		dBm	=	10 log(mW)
W	=	10^dBW/10		dBW	=	10 log(W)

W
mW

=
=

Watts
milliwatts

dB + dB
dBm + dB
dBm + dBm

=
=
=

dB
dBm
nonsense

Range	Radio	Radar
double (2)	+6 dB	+12 dB
half (1/2)	-6 dB	-12 dB

Receiver Noise Power (kTB)
kTB = -174 dBm/Hz T = 300°K (80°F), B = 1 Hz
k T B	= Boltzmann's Constant = 1.380 622 x 10^-23 Watt*sec/°K = Temperature in Degrees Kelvin (°K) = Receiver Noise Bandwidth in Hertz (Hz)

Antenna Gain
dBi	--	decibels (dB's) above or below a Lossless Isotropic Radiator.
dBD	--	decibels above or below a Standard Half wave Dipole antenna with a gain of +2.15 dBi.
dBi = dBD +2.15 dBD = dBi - 2.15

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Constants / Conversions
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