Moody Chart Calculator

Relative Roughness Calculator (ε/D)

Relative roughness (ε/D) is one of two values you need to use the Moody Chart and find friction factor. It compares the height of surface bumps inside a pipe to the pipe's diameter. Enter pipe roughness (in mm) and diameter (in mm) - this calculator does the conversion and gives you the dimensionless ε/D ratio.

Calculate Relative Roughness (ε/D)

Commercial steel = 0.046 mm · PVC = 0.0015 mm · Cast iron = 0.26 mm
mm
Use the internal (bore) diameter, not outer diameter
mm

Results

Relative Roughness (ε/D): -
ε/D (scientific notation): -
Pipe regime on Moody Chart: -
Use in Moody Chart: -

What Is Relative Roughness?

Imagine the inside of a pipe magnified to human scale. The "bumps" on the pipe wall - due to the manufacturing process or the pipe material - are the absolute roughness (ε). A commercial steel pipe has roughness elements about 0.046 mm tall.

Now compare that bump height to the pipe size. In a 10 mm pipe, a 0.046 mm bump is relatively huge - it occupies nearly 0.5% of the pipe radius. In a 1000 mm pipe, the same bump is tiny - just 0.005% of the radius. This ratio - ε/D - is called relative roughness, and it's what actually determines how much extra friction the roughness creates.

The Formula

ε/D = (roughness in mm) / (diameter in mm)

Both ε and D must be in the same units. The result is dimensionless. Use this value directly on the Moody Chart's right-hand axis to select the correct friction factor curve, then read off friction factor at your Reynolds number.

Quick Reference

Material (ε mm)D = 25 mmD = 100 mmD = 300 mm
PVC / Drawn (0.0015)6×10⁻⁵1.5×10⁻⁵5×10⁻⁶
Steel (0.046)1.84×10⁻³4.6×10⁻⁴1.5×10⁻⁴
Galv. Iron (0.15)6×10⁻³1.5×10⁻³5×10⁻⁴
Cast Iron (0.26)1.04×10⁻²2.6×10⁻³8.7×10⁻⁴

Frequently Asked Questions

What ε/D values appear on the Moody Chart?

The Moody Chart typically shows curves from ε/D ≈ 5×10⁻⁶ (essentially smooth) to ε/D = 0.05 (very rough). Values outside this range are rare in practice. The smooth pipe line (ε/D → 0) is the bottom curve; rougher pipes have higher friction factors at the same Reynolds number.

What if my ε/D is very small (below 10⁻⁵)?

Very small ε/D values (e.g., smooth plastic or glass) mean the pipe behaves like a hydraulically smooth pipe across most practical Reynolds number ranges. In the Moody Chart, use the smooth pipe curve or the Blasius equation for smooth turbulent flow: f = 0.316 × Re⁻⁰·²⁵.

Related Tools

📊 Moody Chart Calculator

Enter ε/D and Reynolds number to find the Darcy friction factor.

🔧 Pipe Roughness Calculator

Look up absolute roughness ε by pipe material - then calculate ε/D here.

🌊 Reynolds Number Calculator

The other Moody Chart input - pair with ε/D to find friction factor.

📐 Swamee-Jain Calculator

Use ε/D directly in the explicit Swamee-Jain friction factor formula.