Solar Declination Calculator

Work out solar declination instantly with clear inputs, formula shown and shareable results.

About Solar Declination Calculator

Solar declination is the latitude directly beneath the Sun, swinging between plus and minus 23.44 degrees over the year. Cooper's approximation gives it as 23.44 sin(360(284+n)/365). At the March equinox it is near zero, so the noon Sun stands at 90 minus latitude - 45 degrees at 45 degrees north.

Formulas

Cooper's declination

declination = 23.44 sin(360(284 + n) / 365)

Noon altitude

altitude = 90 - |latitude - declination|

Worked example

With the default values below, Solar Declination Calculator returns Solar Declination of -0.404. Change any input above and every figure here is recalculated in your browser.

Inputs used

Date: 2026-03-21
Latitude for contextaccepts -90–90 deg: 45 deg

Results

Solar Declination: -0.404 deg
Day Of The Year: 80
Solar Altitude At Local Noon: 44.60 deg
Seasonal Position: Near an equinox

Step by step

1Values used
2Cooper's declination
3Noon altitude
4Solar Declination= -0.404 deg
5Day Of The Year= 80
6Solar Altitude At Local Noon= 44.60 deg
7Seasonal Position= Near an equinox

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why 23.44 degrees?

That is Earth's current axial tilt. It varies between about 22.1 and 24.5 degrees over a 41,000 year cycle.

How accurate is Cooper's formula?

Within about 0.3 degrees, which is ample for solar design. Ephemeris calculations are needed for arcsecond precision.