How this calculation works
Find the area swept by the radial segment of an Archimedean spiral.
THE FORMULA
A=b²(θ₂³−θ₁³)/6 for r=bθA worked example
For b=2 and 0≤θ≤1, the area is 4/6.
Good to know
For intervals longer than one turn, overlapping regions are counted with multiplicity.
Reference: OpenStax Calculus Volume 3 (opens in a new tab) ↗
Read the result
Find the area swept by the radial segment of an Archimedean spiral.
The primary result is labeled “Swept area”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
For intervals longer than one turn, overlapping regions are counted with multiplicity.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
For b=2 and 0≤θ≤1, the area is 4/6.
Which rule does this calculator apply?
A=b²(θ₂³−θ₁³)/6 for r=bθ