Basic Rocket Equations

Understanding Space: An Introduction to Astronautics, Revised Edition by Jerry Jon Sellers
One of the most important equations you will encounter in rocketry is Konstantin Tsiolkovsky's “Rocket Equation”; given below.
Δv = V_{E} * ln(M_{L} / M_{E})
Where:
Δv = Final velocity (Deltavee or Δv) of the rocket in meters per second or feet per second.
V_{E}: Velocity of the rocket's exhaust in meters per second or feet per second.
M_{L}: Total mass of the rocket fully loaded (with payload, propellant, etc).
M_{E}: Empty mass of the rocket at burnout with all propellant expended.
The Mass Equation
Mb and Me can be in pounds, kilograms, grams, or tons as long as both use the same unit!
F_{Thrust} = (ṁ * V_{exit}) + A_{exit }* (P_{Exit} – P_{Atm})
Where
F_{Thrust}
= Thrust in Newtons (N)
ṁ
= Mass flow rate in kilograms per second (kg/s)
V_{exit}
= Exit velocity of exhaust in m/sec
A_{exit}
= Exit Area of Nozzle in square meters
P_{Exit}
= Exit Pressure in N/m^{2} (Pascals)^{}P_{Atm}
= Atmospheric Pressure in N/m^{2} (Pascals)
P_{F} = T / V_{E}
P_{F} = Propellant flow in kg/sec.
T = Thrust in Newtons
V_{E} = Exhaust Velocity of Engine in m/sec.
EXAMPLE: The Space Shuttle Main Engine (SSME) has a ISP of 452 seconds (4,434.12 m/sec exhaust velocity) in vacuum and a thrust of 2.18 meganewtons. What is the propellant flow in kg/sec? 2,180,000 N / 4,434.12 m/sec = 491.64 kg/sec P_{F}. 
ISP = (Thrust * Time) / M_{Prop}
Where:
ISP = Specific Impulse of the Propellant/Engine System
Thrust = Thrust of the engine in force.
Time = Length of time the engine operates in seconds.
M_{Prop} = Mass of propellant consumed by the engine during it's operation
Note: All units must be internally consistent; e.g. if you use pounds of thrust, you must also measure propellant consumption in pounds.
EXAMPLE: We have a solid rocket motor which burns for 15 seconds, producing 24,000 lbs of thrust; consuming 1,400 lbs of propellant in the process. (24,000 * 15) / 1,400 = 257.14 ISP 
ISP = V_{E} / 9.81 m/sec2 (Metric)
ISP = V_{E} / 32.2 ft/sec2 (Standard)
Where:
ISP = Specific Impulse
V_{E} = Exhaust Velocity (m/sec or feet/sec)
EXAMPLE: We have an engine that has an exhaust velocity of 8,093 meters per second. What is it's ISP? 8,093 / 9.81 = 824.97 ISP 
V_{E} = ISP * 9.81 m/sec^{2} (metric)
V_{E} = ISP * 32.2 feet/sec^{2} (Standard)
Where:
V_{E} = Exhaust Velocity of the engine in meters per second or feet per second.
ISP = Specific Impulse of the engine.
EXAMPLE: We have an engine that has an ISP of 400. What is its exhaust velocity in m/sec? 400 * 9.81 = 3,924 m/sec Exhaust Velocity 
ΔT = [ (M_{L} * E_{V}) / F ] * [1 – EXP[(ΔV / E_{V})]
Where:
ΔT = Length of burn in seconds
M_{L}: Total mass of the rocket at the beginning of the burn.
E_{V} = Exhaust Velocity in meters/second.
F: Thrust of the rocket in Newtons.
ΔV = DeltaV of burn in meters/second.
EXAMPLE: The Apollo 11 CSM Columbia is executing her TransEarthInjection (TEI) Burn to return to earth with the following key parameters: Velocity Change (ΔV): 3,279 fps (999.444
m/sec) How long will the TEI burn take? [ (16,767.35 * 3080.34) / 91200 ] * [1 – EXP[(999.444 / 3080.34)] = 156.9192 seconds This compares favorably with the actual 151.4 second burn that Apollo 11 executed to return to Earth. 
ΔP = M_{L} – [ M_{L} / EXP( ΔV / E_{V} ) ]
Where:
ΔP = Amount of propellant consumed in kilograms.
M_{L}: Total mass of the rocket at the beginning of the burn.
ΔV = DeltaV of burn in meters/second.
E_{V} = Exhaust Velocity in meters/second.
EXAMPLE: The Apollo 11 CSM Columbia is executing her TransEarthInjection (TEI) Burn to return to earth with the following key parameters: Velocity Change (ΔV): 3,279 fps (999.444
m/sec) How much propellant will the TEI burn consume? 16767.35 – [ 16767.35 / EXP( 999.444 / 3080.34 ) ] = 4645.925 kilograms This compares very favorably with Apollo 11’s TEI Burn, which consumed 10,173 lbs (4,614.4 kg) of propellant, leaving the CSM with a end of burn mass of 26,792.7 lbs (12,153 kg). 