MAC Calculator (Tapered Wing)
Enter your wing dimensions below. Use any unit system (meters, feet, inches), but keep units consistent for all chord and span values.
Assumes a straight, linearly tapered wing panel. Complex multi-panel or cranked wings require segment-by-segment integration.
What is mean aerodynamic chord?
The mean aerodynamic chord (MAC) is a reference chord length used in aircraft stability, control, and weight-and-balance analysis. It is the chord at which aerodynamic forces can be considered to act for many practical calculations, especially for wings that taper from root to tip.
Designers and pilots often use MAC to express center-of-gravity position as a percentage, like 25% MAC or 30% MAC. This standardizes longitudinal stability calculations across wings that do not have constant chord lengths.
How this MAC calculator works
This calculator is based on the classic formula for a trapezoidal wing with linear taper:
Taper ratio: λ = Ct / Cr
Mean aerodynamic chord:
MAC = (2/3) × Cr × (1 + λ + λ2) / (1 + λ)
Wing area: S = b × (Cr + Ct) / 2
Spanwise MAC location from centerline:
yMAC = (b/6) × (1 + 2λ) / (1 + λ)
Optional leading-edge x-location of MAC:
xLE,MAC = yMAC × tan(ΛLE)
Inputs explained
- Root chord: Chord length where wing meets the fuselage.
- Tip chord: Chord length at wing tip.
- Wingspan: Full tip-to-tip span.
- Leading-edge sweep: Angle of wing leading edge relative to a line perpendicular to fuselage centerline (optional).
Why MAC matters in real design work
MAC appears everywhere in aircraft preliminary sizing and flight testing. It is commonly used to:
- Set and communicate center-of-gravity limits.
- Estimate static margin and longitudinal stability.
- Compare loading configurations consistently.
- Place fuel tanks, payload, and landing gear with better balance awareness.
Example quick calculation
Suppose your wing has a 1.8 m root chord, 0.9 m tip chord, and 12 m span. The taper ratio is 0.5. Plugging that into the equation gives MAC = 1.4 m. That single value can then be used to convert CG location into percent MAC, which is usually how flight manuals and design reports present stability limits.
Common mistakes to avoid
- Mixing units (for example inches for chord and meters for span).
- Applying trapezoidal formulas to wings with multiple geometric breaks without segmenting.
- Using projected span for one formula and actual span for another.
- Confusing mean geometric chord with mean aerodynamic chord.
When to use a more advanced method
If your wing has strong twist, multiple taper sections, winglets, or unusual planform geometry, a single closed-form MAC equation may not be accurate enough. In that case, use a CAD-integrated aerodynamic tool or compute MAC through numerical integration over the full planform.
Final note
This mean aerodynamic chord calculator is a practical engineering shortcut for straight tapered wings. It is ideal for conceptual design, student projects, and fast performance checks. For certification-level work, always validate with your full aerodynamic model and structural geometry definitions.