BfX Logo

Understanding Rifle Cant

Ballistics for Excel — Technical Documentation
Home Technical Guide Back to Help
Home
About BfX
Install/Update
Downloads
Excel/VBA settings
Entering formulas
Drag functions
Creators
Help Reference
Units & Drag
Rifle Cant Math

When precision shooting at longer ranges, keeping the rifle perfectly vertical is critical. If a rifle is tilted or "canted" to the side while firing, the trajectory of the bullet shifts in both elevation and windage. Understanding and correcting for rifle cant is essential for repeatable first-round hits.

Assumptions and Limitations

  • Target Plane Projection: This routine assumes that the distance to the target (x) is vastly larger than the vertical (z) and horizontal (y) trajectory offsets.
  • Small-Angle Approximation: Under this approximation, the 3D angular rotation of the bore axis around the optical Line of Sight (LOS) is mathematically treated as equivalent to a 2D planar rotation on the face of the target board.
  • Rigid Sight-Bore Geometry: The drop compensation (d) and sight height (s) are modeled along the true vertical gravity vector, as gravity acts independently of the rifle's roll angle.

Geometric Derivation

The diagram below breaks down the spatial components of rifle cant, showing how an intended hold-right or elevation offset transforms when the rifle is rolled by an angle t (clockwise/right cant).

Rifle Cant Geometric Derivation

Based on the geometric relationships in the target plane:

  • d = drop compensation
  • s = sight height above bore axis
  • h = the impact of the bullet above the line of sight/point of aim

The total height z the bore axis points above the point of aim:

z = d + s + h

The vertical z' after cant (sight rotation around point of aim) with an angle t:

z' = z cos t − y sin t

Change in z due to cant:

Δz = z' − z = z cos t − y sin t − z
Δz = z(cos t − 1) − y sin t

The elevation e before rotation is e = zx [rad] and the windage w is w = yx where x is the distance to the target.

Hence the effective change in elevation is:

Δe = Δzx = zx (cos t − 1) − yx sin t
Δe = e(cos t − 1) − w sin t

The horizontal coordinate y' of the bore axis intersection point after cant:

y' = y cos t + z sin t
Δy = y' − y = y(cos t − 1) + z sin t

Or, expressed as an angle:

Δw = Δyx = yx (cos t − 1) + zx sin t
Δw = w(cos t − 1) + e sin t

Implementation in BfX Add-in

The BfX Excel add-in provides dedicated functions to calculate these corrections automatically. By default, all angular inputs and outputs are in radians.

  • BfX_CantShiftE(e; w; t) — Calculates the vertical elevation delta caused by rifle cant.
  • BfX_CantShiftW(e; w; t) — Calculates the horizontal windage deflection delta caused by rifle cant.

Arguments:

  • e = Initial elevation angle
  • w = Initial windage angle
  • t = Cant angle (t > 0 indicates a clockwise/right cant)

Unit Conversions: Like most BfX functions, you can specify different units (e.g., MOA, MRAD, Degrees) directly in the function string. For example, to calculate the elevation shift in MOA when canting 5 degrees, you would use: =BfX_CantShiftE("moa"; e; w; 5; "deg").
Warning: The use of BfX is entirely your responsibility. It is free to use in private and non-commercially. © 2026 Lydia Lisa Meijer, Netherlands