Cycle Length Calculator
Enter any span of time, in whichever unit you like, and see it in every other unit and as a multiple of each astronomical cycle: how many lunar months, Saros cycles, or Great Years fit inside it. The nearest cycles to your span are surfaced automatically.
Runs entirely in your browser; nothing you type is sent anywhere. Cycle lengths are the mean values from the catalog of astronomical cycles by length.
What the answer means
The calculator does two different jobs with your span, and they are worth reading separately.
In every unit restates the span in ordinary clock and calendar units. These are conventional units, not astronomical ones: a month here is a Julian year divided by twelve, about 30.44 days, and a year is the Julian year of exactly 365.25 days. Those are the units of timekeeping arithmetic, and they are deliberately distinct from the tropical year of 365.2422 days or the synodic month of 29.530589 days further down the page, which are measured from the sky.
As a multiple of each cycle divides your span by each cycle's mean period. A result near a whole number means the span is close to a whole number of turns of that cycle, which is what makes a recurrence: eighteen years and eleven days is very nearly 223 synodic months, and that near-coincidence is the Saros, the reason a similar eclipse returns on that beat. A result near a simple fraction, a half or a third, points at a related rhythm rather than a return.
Every period used here is a mean value. Real intervals vary from one cycle to the next, so a multiple that lands one part in a thousand from a whole number is telling you about the long-run average, not about a particular eclipse or a particular full moon. For dated events, use the Eclipse Explorer or the Moon phase calendar, which compute individual instants from a full ephemeris.
Worked examples
A few spans worth trying, and what they show:
- 18 years lands within a fraction of a percent of one Saros, the eclipse repeat cycle, and close to one lunar nodal cycle of 18.61 years. Two different mechanisms sit at nearly the same length.
- 19 years is almost exactly 235 synodic months: the Metonic cycle, which is why the Moon's phases return to nearly the same calendar dates after nineteen years.
- 8 years is five Venus synodic periods to better than a percent, the near-commensurability that draws the pentagram of Venus.
- One human lifetime, say 80 years, is about four great conjunctions of Jupiter and Saturn, and roughly seven sunspot cycles.
- 26,000 years is close to one turn of axial precession, the Great Year that carries the pole star from Polaris to Vega and back.
Frequently asked questions
What does the cycle length calculator do?
It takes any span of time, from seconds up through years, and expresses it as a multiple of each astronomical cycle in the CycleCalcs catalog, from the lunar month to the precession of the equinoxes. It also surfaces the cycles closest in length to the span you entered.
Where do the cycle lengths come from?
From the same catalog the whole site uses: mean values from standard astronomical references, computed from mean orbital elements near the J2000.0 epoch. Each length is stated on the catalog page along with what the cycle measures.
Does the calculator send my input anywhere?
No. The arithmetic runs entirely in your browser and nothing you type leaves your device. With JavaScript off, every period is still stated on the catalog page, so the reference itself never depends on a script.
Keep exploring
- The Cycle Explorer: the hub for the whole Cycles section, with a live sky panel and a search over every cycle.
- Astronomical Cycles by Length: the full catalog this calculator computes against.
- Synodic Period Calculator: how often any two planets meet, from their orbital periods.
- Date Calculator: the exact span between any two dates, in every unit.
- All calculators: every calculator on the site, one page.