Wave Period and Speed Calculator

Wave period is the time in seconds between successive crests passing a fixed point, and it is one of the two numbers that matter most in a surf forecast. A longer period means faster waves, more power behind them, and generally better surf.

In deep water, wave speed and wavelength are set entirely by period:

Phase speed (m/s) = g × T / (2π) = 1.56 × T Wavelength (m) = g × T² / (2π) = 1.56 × T²

Where:

• T = wave period in seconds
• g = 9.81 m/s² (gravitational acceleration)

Notice that speed scales with the period but wavelength scales with the square of it. Double the period and the waves move twice as fast while sitting four times as far apart.

Two speeds, and forecasters use the slower one

A deep-water swell has two speeds and mixing them up is the single most common mistake in reading a forecast.

Phase speed is how fast an individual crest moves. That is the number the formula above gives you, and it is what this page reports as the headline.

Group speed is how fast the swell train as a whole moves, and in deep water it is exactly half the phase speed. Watch a swell group closely and you will see crests appear at the back, roll forward through the group, and vanish off the front. The energy stays with the group.

Since the energy is the surf, arrival forecasting always uses group speed. A 12-second swell has crests moving at 67 km/h but delivers its energy at 34 km/h, which is what the swell travel time page uses to work out when a storm’s waves reach you. Use the phase speed there and you will predict the swell arriving in half the time it actually takes.

Period guide for surfers:

• Under 8 seconds: Local wind swell. Short, choppy, close together. Weak and difficult to surf.
• 8–10 seconds: Average swell. Reasonable surf for most breaks.
• 10–13 seconds: Good groundswell. Powerful, well-organised waves. Most breaks light up.
• 13–16 seconds: Excellent long-period swell. Strong, long-breaking waves. Big wave spots come alive.
• 16–20+ seconds: Major groundswell. Can travel thousands of kilometres from storms. World-class conditions at appropriate breaks.

Energy scales with the square of the height, so a 2-metre wave carries roughly four times the energy of a 1-metre wave. Power, the rate that energy lands on your beach, is energy times group speed, so it scales with height squared and period together. That is why a modest-looking long-period swell hits so much harder than the buoy number suggests.

Shoaling and breaking: in shallow water waves slow down and stand up. The ratio of wave height to water depth at the moment of breaking is about 0.78, so a wave breaks when the depth is roughly 1.3 times its height. A 2 m wave breaks in about 2.6 m of water. This is why a reef or a sandbar at a particular depth produces a consistent break: the bathymetry picks the wave size that will break there.