Conversion Factors

Constants

π = 3.14159...

e = 2.71828...

Length

1 inch = 2.54 cm 1 meter = 39.37 inch = 3.281 feet

1 foot = 0.3048 meter 12 inches = 1 foot

3 feet = 1 yard 1 yard = 0.9144 meter

1 kilometer = 0.621 mile 1 mile = 1.609 kilometer

1 mile = 5280 feet 1 Å = 10-10 meter

1 μm = 1 μ = 10-6 m = 104 Å 1 lightyear = 9.461 x 1015 m

Area

1 m2 = 106 cm3 = 10.76 ft2 1 ft2 = 0.0929 m2 = 144 inches2

1 inches = 6.452 cm2

Angle

1 radian = 57.296 degrees

1 degree = 0.0175 radian

Volume

1 m3 = 10 cm3 = 6.102 x 104 inches3

1 ft3 = 1728 inches3 =2.83 x 10-2 m3

1 liter = 1000 cm3 = 1.0576 qt = 0.0353 ft3

1 ft3 = 7.481 gal = 28.32 liters = 2.832 x 10 m3

1 gal = 3.786 liters = 231 inches3

Mass

1000 kg = 1 t (metric ton) 1 slug = 14.59 kg

1 u = 1.66 x 10-27 kg

Force

1 N = 105 dyne = 0.2248 lb 1 lb = 4.448 N

1 dyne = 10-5 N = 2.248 x 10-6 lb

Velocity

1 mi/h = 1.47 ft/s = 0.447 m/s = 1.61 km/h

1 m/s = 100 cm/s = 3.281 ft/s 1 mi/min = 60 mi/h = 88 ft/s

Acceleration

1 m/s2 = 3.28 ft/s2 = 100 cm/s2 1 ft/s2 = 0.3048 m/s2 = 30.48 cm/s2

Pressure

1 bar = 105 N/m2 = 14.50 lb/inches2 1 atm = 760 mm Hg = 76.0 cm Hg

1 atm = 14.7 lb/inches2 = 1.013 x 105 N/m2

1 Pa = 1 N/m2 = 1.45 x 10 lb/inches2

Time

1 year = 365 days = 3.16 x 107 s

1 day = 24 h = 1.44 x 103 min = 8.64 x 104 s

Enegry

1 J = 0.738 ft*lb = 107 erg 1 cal = 4.186 J

1 Btu = 252 cal = 1.054 x 103 J 1 eV = 1.6 x 10-19 J

931.5 MeV/c2 = 1 u 1 kWh = 3.60 x 106 J

Power

1 hp = 550 ft*lb/s = 0.746 kW 1 W = 1 J/s = 0.738 ft*lb/s

1 Btu/h = 0.293 W

Trignometry Formulas

Identities

csc t = 1/sin t sec t = 1/cos t

cot t = 1/tan t tan t = sin t/cos t

cot t = cos t/sin t sin2 t + cos2 t = 1

1 + tan2 t = sec2 t 1 + cot2 t = csc2 t

Addition Formulas

sin(u + v) = sinu cosv + cosu sinv

cos(u + v) = cosu cosv = sinu sinv

tan(u + v) = (tanu + tanv)/(1 – tanu tanv)

Subtraction Formulas

sin(u – v) = sinu cosv = cosu sinv

cos(u – v) = cosu cosv + sinu sinv

tan(u – v) = (tanu – tanv)/(1 + tanu tanv)

Formulas for Negatives

sin(-t) = -sin t csc(-t) = -csc t

cos(-t) = cos t sec(-t) = sec t

tan(-t) = -tan t cot(-t) = -cot t

Double Angle Formulas

sin 2u = 2sinu cosu

cos 2u = cos2 u – sin2 u = 1 – 2sin2 u = 2cos2 u - 1

Half Angle Identities

sin2 u = (1 – cos 2u)/2

cos2 u = (1 + cos 2u)/2

tan2 u = (1 – cos 2u)/(1 + cos 2u)

Half Angle Formulas

sin u/2 = + sqrt[(1 – cos u)/2]

cos u/2 = + sqrt[(1 + cos u)/2]

tan u/2 = (1 – cos u)/sin u = sin u/(1 + cos u)

Cofunction Formulas

sin(π/2 – u) = cos u csc(π/2 – u) = sec u

cos(π/2 – u) = sin u sec(π/2 – u) = csc u

tan(π/2 – u) = cot u cot(π/2 – u) = tan u

Product To Sum Formulas

sinu cosv = ½[sin(u + v) + sin(u – v)]

cosu sinv = ½[sin(u + v) – sin(u – v)]

cosu cosv = ½[cos(u + v) + cos(u – v)]

sinu sinv = ½[cos(u – v) – cos(u + v)]

Sum To Product Formulas

sinu + sinv = 2sin[(u+v)/2] cos[(u-v)/2]

sinu – sinv = 2cos[(u+v)/2] sin[(u-v)/2]

cosu + cosv = 2cos[(u+v)/2] cos[(u-v)/2]

cosu – cosv = -2sin[(u+v)/2] sin[(u-v)/2]

Algebra formulas

Quadratic Formula

If ax2 + bx + c = 0, then x = (-b + sqrt(b2 – 4ac))/2a.

(where a, b, c are constants & a not equal to 0)

Exponents and Radicals

axay = ax + y a1/x = x√a

(ax)y = axy ax/y = y√ax

(ab)x = axbx ax/y = ( y√a)x

(a/b)x = ax/bx x√ab = x√a x√b

ax/ay = ax-y x√(a/b) = x√a/x√b

a-x = 1/ax xy√a = xy√a

Absolute Value

|x| < style=""> if and only if -a

|x| > a if and only if either x>a or x<-a

Special Product Formulas

(x + y)(x – y) = x2 – y2

(x + y) 2 = x2 + 2xy + y2 (x – y) 2 = x2 – 2xy + y2

(x + y)3 = x3 + 3xy2 + 3xy2 + y3 (x – y) 3 = x3 – 3xy2 + 3xy2 – y3

Binomial Theorem

(x + y)n = x n + (n1)x n-1 y + (n2)x n-2 y 2 + ... + (nk)x n-k y k + ... + y n,

where (nk) = n!/k!(n – k)!

Special Factoring Formulas

X2 – y2 = (x + y)(x – y)

x2 + 2xy + y2 = (x + y)2 x2 – 2xy + y2 = (x – y) 2

x3 – y3 = (x – y)(x2 + xy + y2) x3 + y3 = (x + y)(x2 – xy + y2)

Inequalities

If a>b and b>c, then a>c.

If a>b, then a+c>b+c.

If a>b and c>0, then ac>bc.

If a>b and c<0,>

Exponentials and Logarithms

y = logax ó ay = x logaxy = logax + logay

loga (x/y) = logax – logay logaxr = rlogax

alogax = x logaax = x

loga1 = 0 logaa = 1

logx = log10x lnx = logex

logbu = logau/logab

DASAVATARAM

DASAVATARAM