HesapHanem

Cylindrical to Cartesian Converter

Cartesian x, y and z for a cylindrical point, rounded to two decimals.

How it is calculated

The converter reads three numbers: the radius r (distance from the z-axis), the angle θ in degrees, and the height z. It first turns the angle into radians, t = θ × π / 180, then computes x = r·cos(t) and y = r·sin(t). The height is passed through unchanged, and if you leave z empty it is treated as 0. All three results are rounded to two decimals, so a value that should be exactly zero (such as x at 90°) shows as 0.00. A negative radius is accepted and simply points the opposite way (the same as adding 180° to the angle), and angles beyond 360° wrap around naturally.

Worked example

Take r = 5, θ = 30° and z = 2. Convert the angle: 30 × π / 180 ≈ 0.5236 rad. Then x = 5 × cos(30°) = 5 × 0.8660 = 4.33, and y = 5 × sin(30°) = 5 × 0.5 = 2.50. The height carries over, so z = 2.00. The Cartesian point is (4.33, 2.50, 2.00).

Try this example →

Common mistakes

  • Entering the angle in radians. The field expects degrees, so 1.57 is treated as a bit under 2 degrees, not a quarter turn.
  • Mixing up the roles of r and z: r is the distance from the axis in the xy-plane, not the straight-line distance from the origin (that is the spherical radius).
  • Measuring θ from the y-axis. Here it is measured counter-clockwise from the positive x-axis.
  • Expecting z to change. Cylindrical and Cartesian share the same z, so it is only reformatted.
  • Reading a rounded 0.00 as an exact zero when the inputs were not clean angles; the displayed values are rounded to two decimals.

About this calculator

Cylindrical coordinates locate a point by radius r (distance from the z-axis), angle θ (measured from the x-axis in the xy-plane), and height z. Converting to Cartesian (x, y, z) uses x = r·cos(θ), y = r·sin(θ), and z stays unchanged, giving a point's position in the standard rectangular system.

This conversion is routine in mechanical and electrical engineering, robotics, and 3D graphics, wherever a system is naturally described with a radius and rotation angle — such as a machined part on a lathe, a robotic arm's swing, or a magnetic field around a wire — but needs to be combined with Cartesian data from CAD models or physics simulations.

Was this helpful?

You can pick up to 3 reactions.

Comments

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators