Capillary Rise Calculator

Summary

Calculate the height a liquid rises or falls in a capillary tube using surface tension, contact angle, density, and tube radius.

How it works

1. Enter the liquid's surface tension γ (N/m). Water at 20 °C is about 0.0728 N/m.
2. Enter the contact angle θ in degrees. Angles below 90° cause rise; angles above 90° cause depression.
3. Enter the liquid's density ρ (kg/m³). Water is 1000 kg/m³; mercury is 13 600 kg/m³.
4. Enter the tube's inner radius r (m). Use small values like 0.0005 m (0.5 mm) for visible capillary action.
5. Gravitational acceleration g defaults to 9.81 m/s² but can be changed for other planets.
6. Click Calculate. The tool applies h = (2γ cos θ) / (ρ g r) and shows the height in meters, centimeters, and millimeters.

Use cases

• Verify capillary rise experiments in physics or chemistry lab courses.
• Select the correct capillary tube radius for a target liquid height.
• Understand how surface tension affects water transport in soil and plants.
• Explore why mercury is depressed in glass capillaries (contact angle > 90°).
• Compare capillary behavior of different liquids at a given tube radius.
• Estimate rise height when designing microfluidic channels.

Frequently Asked Questions