Calculations in a logarithmic spiral. With this form of spirals, the radius increases proportionally with the spiral length. So the distance between two turnings increases with each turning for the factor f. The shape parameter determines the spiral's shape, this value mostly if far less than 1. It is easier to use the growth factor instead. The distance from the spiral start to the origin matches the size parameter a. Enter radius, number of revolutions or angle and shape parameter or growth factor. Choose the number of decimal places, then click Calculate. Please enter angles in degrees, here you can convert angle units.

Formulas:
r = a * e^{k*φ}
n = φ / 360°
f = ( e^{2π} )^{k}
l = ( r - a ) / sin( arctan(k) )
p = l + r for n≤1
p = r - a * e^{k*(φ-360°)} + l - ( a * e^{k*(φ-360°)} - a ) / sin( arctan(k) ) for n>1
d = r + a * e^{k*(φ-180°)} for φ>180°
h = a * ( e^{k*(φ-90°)} + e^{k*(φ-270°)} ) für φ>270°
ρ = r / cos( arctan(k) )
A = ( r² - a² ) / (4k)

pi:
π = 3.141592653589793...

Radius, parameter a, length, perimeter and diameter have a one-dimensional unit (e.g. meter), the area has this unit squared (e.g. square meter). The number of turnings, the shape parameter and the growth factor are dimensionless.