Induced Drag Coefficient Calculator
Induced drag is the drag penalty paid for generating lift. It results from wingtip vortices that create downwash across the wing, tilting the local aerodynamic force rearward. The induced drag coefficient (CDi) is computed using Prandtl's lifting line theory: CDi = CL^2 / (pi x e x AR), where e is the Oswald efficiency factor and AR is the wing aspect ratio. This calculator also computes the induced drag force given wing area and dynamic pressure, and estimates the L/D ratio contribution from induced drag.
Induced drag coefficient formula (Prandtl)
CDi = CL^2 / (pi x e x AR)
CD_total = CD0 + CDi
L/D = CL / CD_total
Induced Drag Force (N) = CDi x q x S
This formula is derived from Prandtl's lifting line theory (1918-1919) for finite wings. The formula assumes attached flow below stall and subsonic conditions. The Oswald factor e accounts for deviation from the ideal elliptical lift distribution. For a perfect elliptical wing, e = 1.0 and CDi reaches its theoretical minimum for a given CL and AR.
Reducing induced drag in practice
- Increase aspect ratio: each doubling of AR halves CDi. High-aspect-ratio wings are used on long-range aircraft and sailplanes.
- Winglets: by diffusing the wingtip vortex, winglets effectively increase the aerodynamic span, raising the Oswald factor e.
- Fly faster at cruise: CDi varies as CL^2, so flying faster (lower CL) significantly reduces induced drag at the cost of higher profile drag. Optimal cruise speed balances these two.
- Elliptical lift distribution: the classic Spitfire elliptical wing minimizes induced drag for a given span but is complex to manufacture. Modern wings approximate elliptical loading with twist.
Induced drag coefficient calculator: frequently asked questions
What is induced drag?
Induced drag (also called lift-induced drag or vortex drag) is the aerodynamic drag that arises as a consequence of generating lift. When a wing produces lift, it also creates trailing vortices at the wingtips. These vortices produce a downwash that tilts the local lift vector rearward, creating a drag component. Induced drag increases with lift coefficient and decreases with wing aspect ratio.
What is the induced drag coefficient formula?
CDi = CL^2 / (pi x e x AR), where CL is the lift coefficient, e is the Oswald span efficiency factor (0 to 1), and AR is the wing aspect ratio (wingspan^2 / wing area). This formula was derived by Ludwig Prandtl in his lifting line theory and is fundamental to finite wing aerodynamics.
What is the Oswald efficiency factor?
The Oswald efficiency factor (e, also written e0) accounts for non-elliptical lift distribution and other induced drag penalties. A perfect elliptical wing has e = 1.0. Real wings typically have e = 0.75 to 0.95. Wings with winglets or swept tips tend to have higher e. Fuselage and interference effects reduce e below the isolated wing value.
What is wing aspect ratio and how does it affect induced drag?
Aspect ratio (AR) = wingspan^2 / wing area, or equivalently = wingspan / mean chord. Longer, narrower wings have higher AR and lower induced drag for the same CL. High-performance sailplanes have AR of 25-40. Commercial airliners are typically AR = 8-12. Fighter jets with short, swept wings may have AR = 2-4. Induced drag is inversely proportional to AR, so doubling AR halves CDi.
How does induced drag relate to total drag?
Total drag coefficient CD = CD0 + CDi, where CD0 is zero-lift (profile or parasite) drag. At low speeds and high CL, induced drag dominates. At high speeds and low CL, profile drag dominates. The speed for minimum total drag (best L/D speed) occurs where CD0 = CDi, giving the maximum range for propeller aircraft and the maximum endurance for jet aircraft.
Official sources
- NASA Glenn Research Center: Induced Drag Coefficient (NASA Glenn).
- NASA Technical Report Server: NASA TM-80210: Applied Aerodynamics of Wings.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.