Lift Curve Slope Calculator

Calculator Inputs

Analysis mode

Choose whether to include finite-span wing effects.

Section slope method

Auto starts from 2π per radian before optional corrections.

Custom baseline slope

Used only when custom slope mode is selected.

Custom slope unit

Per-degree values are converted internally.

Aspect ratio

Ignored if both span and area are entered.

Wing span

Optional. Used with area to compute aspect ratio.

Wing area

Optional. Use the same unit system as span.

Efficiency factor e

Typical practical values are about 0.75 to 0.98.

Mach number

Subsonic only in this implementation.

Quarter-chord sweep angle (deg)

A simple cosine correction is applied.

Angle of attack α (deg)

Current operating angle used for CL estimation.

Zero-lift angle αL=0 (deg)

Use 0 for a symmetric section or measured values for cambered sections.

Plot minimum α (deg)

Lower bound for the plotted lift line.

Plot maximum α (deg)

Upper bound for the plotted lift line.

Formula Used

This page uses linear pre-stall aerodynamic relations suitable for quick engineering estimates.

1) Low-speed section slope: a₀ ≈ 2π per radian

2) Subsonic compressibility correction: a₀,M = a₀ / √(1 − M²)

3) Sweep approximation: a₀,swept = a₀,M × cos(Λ)

4) Finite-wing slope: a = a₀,swept / [1 + a₀,swept / (π e AR)]

5) Lift coefficient in the linear range: C_L = a × (α − α_L=0)

Angles are converted to radians for the actual calculation. The sweep correction is approximate, and the model should not be used near stall or in transonic nonlinear flow.

How to Use This Calculator

Select whether you want a two-dimensional airfoil estimate or a finite-wing estimate.
Choose the section slope source. Use the classical baseline or enter a measured custom slope.
For a wing, enter aspect ratio directly or provide span and wing area.
Add efficiency factor, Mach number, sweep angle, current angle of attack, and zero-lift angle.
Set the plot range, then submit the form to see results above the calculator.
Use the CSV button to export inputs, results, and curve data.
Use the PDF button to save the result panel and chart as a printable report.

Example Data Table

Sample case for reference using a finite-wing estimate and the classical baseline section slope.

Case	Mode	AR	e	Mach	Sweep	αL=0	α	Slope /rad	Slope /deg	CL at α
Reference wing	Finite wing	7.80	0.90	0.20	5.0°	-1.0°	5.0°	4.8941	0.0854	0.5125

Frequently Asked Questions

1) What is lift-curve slope?

Lift-curve slope is the rate at which lift coefficient changes with angle of attack. It tells you how strongly a wing or airfoil responds to small attitude changes.

2) Why does aspect ratio matter?

A larger aspect ratio usually reduces induced angle effects and keeps the finite-wing slope closer to the two-dimensional airfoil slope. Shorter wings generally have lower slope.

3) What does the efficiency factor represent?

The efficiency factor captures how closely the wing behaves like an ideal lifting distribution. Lower values usually mean stronger three-dimensional losses and a smaller lift-curve slope.

4) Why is Mach number included?

Subsonic compressibility changes the section lift slope. This page applies a Prandtl-Glauert style correction, which is helpful for preliminary work below the transonic region.

5) How does sweep affect the result?

Sweep generally lowers the component of flow normal to the leading edge, so the effective lift-curve slope is reduced. This page uses a practical cosine approximation.

6) Can I use this calculator near stall?

No. The calculator assumes a linear attached-flow region. Near stall, separated flow and nonlinear behavior dominate, so measured data or a higher-fidelity aerodynamic method is better.

7) Why are there values per radian and per degree?

Aerodynamic theory usually uses radians, while engineers often discuss trends per degree. Showing both helps you compare literature formulas with day-to-day design estimates.

8) When should I enter a custom section slope?

Use a custom value when wind-tunnel data, CFD results, airfoil software, or validated reference data exist for your specific section. That usually improves preliminary accuracy.