Calculate the radius of a cylinder from volume & height, surface area & height, lateral area & height, circumference, or base area. All cylinder properties shown with visual breakdowns.
The radius of a cylinder is the distance from the center of one of its circular ends to the edge. It is one of the two defining dimensions of a right circular cylinder — the other being the height. From the radius and height, every other property of the cylinder can be calculated, including volume, surface area, lateral area, and circumference.
This calculator provides five methods to find the cylinder radius. You can calculate it from volume and height, total surface area and height, lateral area and height, the base circumference, or the base area. Each method rearranges the standard cylinder formulas so you can always find the radius regardless of which measurements you start with.
Cylinders are everywhere in daily life — soda cans, water pipes, grain silos, hydraulic pistons, pencils, and battery cells are all cylindrical. Engineers, students, and hobbyists frequently need to reverse-engineer the radius from known properties. For instance, if you know a pipe's capacity and length, you can find the radius needed to hold that volume.
The key formulas are: volume V = πr²h, lateral surface area LA = 2πrh, total surface area SA = 2πr² + 2πrh, and circumference C = 2πr. For the surface-area method, the calculator solves a quadratic equation to extract the positive root. Use the built-in presets for everyday objects like soda cans, paint cans, and oil drums to see instant results, and consult the reference table for common cylinder sizes.
This calculator is useful when a cylinder is specified by capacity, side area, or circumference instead of direct radius. That happens often with cans, tanks, pipes, piston bores, and storage drums, where you need to recover the cross-sectional size first and then check volume, material usage, or fit against the rest of a design.
r = √(V/(πh)) | 2πr² + 2πrh − SA = 0 (quadratic) | r = LA/(2πh) | r = C/(2π) | r = √(A/π), where V = volume, h = height, SA = surface area, LA = lateral area, C = circumference, A = base area.
Result: Radius = 3.0434 cm
For a 355 cm^3 cylinder with height 12.2 cm, the calculator applies r = sqrt(V / (pi h)). That gives r = sqrt(355 / (pi x 12.2)) = sqrt(9.2624) = 3.0434 cm. The matching diameter is about 6.0869 cm, the lateral area is about 233.2916 cm^2, and the total surface area is about 291.4883 cm^2.
A cylinder is defined by its **base radius r** and **height h**. Its three key measurements are **volume** V = πr²h, **lateral surface area** A_lat = 2πrh (the "label" area), and **total surface area** A_tot = 2πr² + 2πrh = 2πr(r + h). This calculator inverts these formulas across five solve modes: from volume + height, total area + height, lateral area + height, base circumference, or base area.
A classic optimization problem asks: for a fixed volume V, what ratio h/r minimizes total surface area? Setting dA/dr = 0 gives the elegant result h = 2r — the optimal can is as tall as it is wide. Real beverage cans deviate slightly (standard 355 mL cans have r ≈ 3.04 cm, h ≈ 12.2 cm, giving h/r ≈ 4), primarily to fit comfortably in the hand and reduce lid manufacturing cost.
- **From volume and height**: r = √(V / (πh)). Used when the fill volume and container height are specified. - **From total surface area and height**: A_tot = 2πr² + 2πrh. This is quadratic in r: 2πr² + 2πhr − A_tot = 0, solved by the quadratic formula. - **From lateral area and height**: A_lat = 2πrh ⟹ r = A_lat / (2πh). - **From circumference**: C = 2πr ⟹ r = C / (2π). - **From base area**: A_base = πr² ⟹ r = √(A_base / π).
Cylinder radius is calculated in **mechanical engineering** for piston bores, pressure vessel design, and shaft sizing; in **chemical engineering** for reactor and storage tank design; in **civil engineering** for concrete column sizing and caisson foundations. The **hydraulic diameter** D_h = 4A/P for a full circular pipe equals 2r, linking cylinder geometry to fluid mechanics. In **food packaging**, choosing r and h to meet a volume spec while minimizing material cost is a standard optimization exercise. In **medicine**, the radius of blood vessels is central to Poiseuille's law (flow rate ∝ r⁴), explaining why even small reductions in arterial radius dramatically increase resistance.
The radius is the distance from the center of the circular cross-section to the edge. It is the same at every cross-section along the height of a right circular cylinder.
Use r = √(V / (πh)). Divide the volume by π times the height, then take the square root. For example, 355 cm³ with h = 12.2 cm gives r ≈ 3.04 cm.
The total surface area formula SA = 2πr² + 2πrh is a quadratic in r. The calculator solves it automatically — you just need to provide SA and h.
The lateral area is the area of the curved surface only (excluding the two circular ends). It equals 2πrh — imagine unrolling the cylinder into a rectangle of width 2πr and height h.
The radius matters more because volume depends on r² but only linearly on h. Doubling the radius quadruples the volume, while doubling the height only doubles it.
This calculator computes the solid cylinder radius. For a pipe, you would need separate calculations for the outer radius and inner radius, then subtract volumes or areas.