Using the formulas for [[Radius of Turn]] and [[Bank Angle Required for Standard Rate Turn]], the radius of turn at standard rate can be derived:
$
radius = \frac{v^2}{11.26\tan(Φ)}
$
$
Φ = \tan^-¹(\frac{3}{1091}v)
$
substituting the formula for $Φ$ produces:
$
radius = \frac{v^2}{11.26\tan(\tan^-¹(\frac{3}{1091}v))}
$
which reduces to:
$
radius\ (ft) = 32.297v
$
or
$
radius\ (nm) = 0.0053v
$