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

a^xa^y = a^{x + y} a^1/x = _x√a

(a^x)^y = a^xy a^x/y = _y√a^x

(ab)^x = a^xb^x a^x/y = ( _y√a)^x

(a/b)^x = a^x/b^x _x√ab = _x√a _x√b

a^x/a^y = a^x-y _x√(a/b) = _x√a/_x√b

a^-x = 1/a^x _x√_y√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 + ... + (ⁿ_k)x ^n-k y ^k + ... + y ⁿ,

where (ⁿ_k) = 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 = log_ax ó a^y = x log_axy = log_ax + log_ay

log_a (x/y) = log_ax – log_ay log_ax^r = rlog_ax

a^logax = x log_aa^x = x

log_a1 = 0 log_aa = 1

logx = log₁₀x lnx = log_ex

log_bu = log_au/log_ab