🛢️ Cylinder Calculator 2026
Calculate surface area, volume, radius, or height of a cylinder
Enter Radius and Height
r = radius, h = height
📊 Results
Radius
5 cm
Height
10 cm
Diameter
10 cm
Lateral Area
314.16 cm²
Base Area
78.54 cm²
Total Surface
471.24 cm²
Volume
785.4 cm³
📝 Step-by-Step Solution
Given: r = 5 cm, h = 10 cm
Lateral Area = 2πrh = 2π × 5 × 10 = 314.16 cm²
Base Area = πr² = π × 5² = 78.54 cm²
Total Surface = 2πr(r + h) = 2π × 5 × 15 = 471.24 cm²
Volume = πr²h = π × 25 × 10 = 785.40 cm³
📐 Cylinder Formulas
Lateral Surface Area: AL = 2πrh
Base Area: AB = πr²
Total Surface Area: A = 2πr(r + h) = 2πr² + 2πrh
Volume: V = πr²h
Radius from Volume: r = √(V / πh)
Height from Volume: h = V / πr²
Understanding Cylinder Geometry
🛢️ What is a Cylinder?
3D shape with two parallel circular bases connected by a curved surface. Right circular cylinder: bases directly above each other.
📄 Lateral Surface
A = 2πrh. The curved surface only. Unrolls into a rectangle: width = circumference (2πr), height = h.
📐 Total Surface Area
A = 2πr(r + h). Lateral area + two circular bases. Use for material needed to fully enclose cylinder.
📦 Volume
V = πr²h. Base area times height. Measures capacity. Think: circular layers stacked to height h.
Frequently Asked Questions
What is the surface area formula for a cylinder?
Total Surface Area = 2πr(r + h). This equals 2πr² (two bases) +
2πrh (lateral). Where r = radius, h = height.
What is the volume formula for a cylinder?
V = πr²h. Base area times height. Example: r = 5, h = 10 → V = π ×
25 × 10 = 785.4 cubic units.
What is the lateral surface area of a cylinder?
A = 2πrh. The curved surface only (no bases). Opens into a
rectangle with width 2πr and height h.
How do I find radius from volume?
r = √(V / πh). Rearrange volume formula. Need to know height.
Example: V = 785.4, h = 10 → r = √(785.4/31.4) = 5.
How do I find height from volume?
h = V / πr². Rearrange volume formula. Need to know radius.
Example: V = 785.4, r = 5 → h = 785.4/78.5 = 10.
What is the base area of a cylinder?
A = πr². Same as circle area. The cylinder has two identical
circular bases, so total base area = 2πr².
How do I find radius from surface area?
Solve 2πr² + 2πrh = A. This is quadratic in r. Use quadratic
formula: r = (-h + √(h² + A/π)) / 2. Need to know height.
What is the relationship between cylinder and cone?
Cone volume = ⅓ cylinder volume (same base and height). Cylinder
lateral area uses 2πrh; cone uses πrl.
What is a right circular cylinder?
Cylinder with circular base and axis perpendicular to base. Bases
are directly above each other. Most common type; formulas here apply to this.
How do I calculate paint needed for a cylinder?
Use surface area formula. For outside only: 2πrh + πr² (one base
if sitting). For full exterior: 2πr(r + h).
What is the difference between diameter and radius?
Diameter = 2 × radius. Diameter goes all the way across; radius
goes from center to edge. d = 2r.
What are real-world examples of cylinders?
Cans, pipes, tanks, batteries, pillars, drinking glasses, barrels, tree
trunks (approximately).
How does doubling radius affect volume?
Volume increases 4×. V = πr²h so (2r)² = 4r². Doubling height only
doubles volume. Radius has greater impact.
What is a hollow cylinder?
Cylinder with inner and outer radius (like a pipe). Volume = πh(R²
- r²). Surface area includes inner, outer, and ring ends.
How do I find circumference of cylinder base?
C = 2πr = πd. Same as circle circumference. This is the "width" of
the unrolled lateral surface.
What units should I use?
Keep consistent. Area in square units (cm², m²), volume in cubic
units (cm³, m³). All inputs must use same unit.
How accurate is this calculator?
Uses precise mathematical formulas with π to full precision.
Results are mathematically exact.