The lift and drag equations
NASA’s familiar dimensional lift and drag equations are
L = q S CL and D = q S CD, with q = ½ ρ V².
Solving for the coefficients, CL = L / (q S) and CD = D / (q S). The ratio L/D = CL/CD is the aerodynamic efficiency of the condition you entered. In steady level flight L = W, or more generally L = n W, so the required coefficient is CL = n W / (q S).
Worked example
A 1,000 kg vehicle at 50 m/s, S = 10 m², sea-level density 1.225 kg/m³: q = 1,531.25 Pa, W = 9,806.65 N, and the level-flight CL is 0.640. If the measured drag is W/12, then CD = 0.0534 and L/D = 12.
Sources
NASA Glenn Beginner’s Guide to Aeronautics (lift and drag equations); Anderson, Introduction to Flight; FAA Pilot’s Handbook of Aeronautical Knowledge, Chapter 5.
Frequently asked questions
What is q in the lift equation?
q is dynamic pressure, ½ρV². It has the units of pressure. CL and CD are dimensionless.
When is lift equal to weight?
In steady, level, unaccelerated flight, lift equals weight (n = 1). In a level coordinated turn, n = 1/cos φ and the required CL rises by that factor. Climbing, descending, or maneuvering changes the balance of forces.
Can I enter coefficients instead of forces?
Yes. Enter CL and/or CD and the page will compute the corresponding lift and drag at your q and S, and the L/D ratio.