Use the culminating point’s timing
The declination of the ecliptic point at the MC, together with geographic latitude, supplies an ascensional correction. The implementation uses thirds of that correction when choosing the shifted meridian angles, then calculates the eastern horizon intersection at each shift.
These shifted angles are steps in the geometry. They do not change your entered birth time or create additional natal charts. The final cusps describe the selected Koch partition for the original birth inputs.
Why Koch and Placidus can disagree
Both retain the true Ascendant and MC in their supported quadrant construction, but they place intermediate cusps differently. A planet close to one of those cusps can change house when you switch systems, even though its sign, longitude and aspects remain unchanged.
A polar error is not an alternative chart
Sky Degrees refuses Koch at or beyond latitude 90° minus obliquity, in either hemisphere. It also rejects a circumpolar culminating-point construction. It does not substitute Placidus or another system and continue displaying a Koch label. Select a supported alternative explicitly if the requested chart is unavailable.
A CONCRETE EXAMPLE
Worked timing and a boundary comparison
For ARMC 100°, latitude 40° N and obliquity 23.4393°, the ascensional correction is approximately 20.993836°. The intermediate meridian shifts include −73.995891°, −36.997945°, +36.997945° and +73.995891°. These are angular rotation intervals, not zodiac cusp longitudes.
The resulting second cusp is 217.314009°. Placidus gives 214.762346° for the same geometry. An illustrative planet at longitude 215° lies before the Koch second cusp, in house one, but after the Placidus second cusp, in house two. The difference follows from the boundary calculation, not a change in the planet’s position.
Read it in your own chart.
Keep the date, recorded time, location and zodiac visible as you compare results. Guest calculations need no account.
Create your free chartCommon questions
Does selecting Koch alter the MC?
Not when the time, place, zodiac and other astronomical settings remain fixed. The MC is calculated independently of the house-system choice.
Can Koch calculate a chart at 70° N?
With obliquity 23.4393°, 70° N is beyond the supported 66.5607° limit, so this implementation returns an unavailable-house error. It does not produce guessed cusps.
Calculation & interpretation
New personal calculations use Skyfield with JPL DE440 data and the site’s documented house and zodiac rules. The preserved Greenwich teaching chart has its own historical source label. Worked arithmetic and geometry examples are labelled separately. Astrological meanings are symbolic conventions, not established scientific predictions.
Birth time and place affect angles and houses. Unsupported or ambiguous inputs return an error rather than an invented chart. Personal results stay in browser state and do not create public result URLs.
Read the calculation settings guide