New York
America/New_YorkNear the Eastern standard meridian; daylight time creates the larger summer gap.
- January · UTC−05:00
- 12:00 → 11:54:30
- July · UTC−04:00
- 12:00 → 10:57:56
Concept
True solar time: calculator, formula and examples
Turn civil clock time into an inspectable astronomical receipt: historical timezone → longitude correction → equation of time → local apparent solar time.
True solar time, also called local apparent solar time, tracks the actual Sun: local noon occurs when the Sun crosses the observer's meridian.
Live astronomical receipt
Calculate true solar time
Enter a civil date, clock time, and city. The result shows every correction instead of hiding the arithmetic.
Observation receipt
Awaiting coordinates
- Historical timezone
- —
- Coordinates
- —
- Longitude correction
- —
- Equation of time
- —
- Net correction
- —
True solar time—
The Sun-based result will appear here.
Calculate your true solar time now
Use Use device time now to fill your device’s current date and clock reading, or enter another civil time. Then select the place where that reading applies and calculate. The tool works as a true solar time calculator, converter and current-time receipt: it returns the corrected time and exposes the historical timezone, longitude correction and equation of time behind it.
The device button fills only the date and clock reading. It does not assume your physical location or silently reuse the device timezone for another city; you still choose the relevant place before calculating.
The true solar time formula
For a civil clock reading at a known place and date:
True solar time = civil clock time + longitude correction + equation of time
The longitude term is:
Longitude correction (minutes) = 4 × longitude in degrees east − historical UTC offset in minutes
West longitudes and UTC offsets west of Greenwich are negative. The historical offset must include daylight saving time when it was in force. The equation of time is then added as apparent solar time minus mean solar time.
| Quantity | What it accounts for |
|---|---|
| Historical timezone | The legal clock offset, including past DST rules |
| Longitude correction | Where the city sits east or west of that clock meridian |
| Equation of time | The seasonal effect of Earth’s axial tilt and non-circular orbit |
| True solar time | The local apparent position of the real Sun |
The calculator above resolves the city-center coordinates and historical timezone, then uses the Sun’s apparent position rather than a day-of-year shortcut.
Why city results differ
Cities that share a legal timezone can still have different true solar times because longitude changes continuously inside the zone. New York and Boston both use Eastern Time, for example, but Boston sits east of the standard meridian while New York sits slightly west of it during daylight time. Latitude changes the Sun’s height and day length; the clock correction shown here is driven by longitude, the historical UTC offset and the date-specific equation of time.
The reviewed city references below keep that distinction inspectable. Each location page runs the calculator in place and publishes exact January and July receipts; it is not a redirect into a generic form. This page remains the single formula and unqualified true solar time calculator reference.
Worked example: Toronto at noon
Take 20 July 2026 at 12:00 in Toronto. Daylight saving time is active, so the civil offset is UTC−04:00. Using the city-center longitude of 79.399° W:
| Step | Result |
|---|---|
| Civil clock time | 12:00:00 |
| Longitude correction | −77.59 min |
| Equation of time | −6 min 25 sec |
| Net correction | about −84.0 min |
| True solar time | 10:35:59 |
The large summer difference is not an error: daylight saving time advances the civil clock by one hour, while Toronto also lies west of the UTC−04:00 reference meridian. Change the date to winter in the live calculator and the historical offset changes with it.
Apparent solar time vs mean solar time
Local mean solar time uses longitude but smooths the solar day to a uniform 24-hour average. Local apparent solar time, commonly called true solar time, follows the real Sun. A sundial approximates apparent solar time; a longitude-adjusted uniform clock gives mean solar time.
The gap between apparent and mean solar time is the equation of time. It varies through the year because Earth’s axis is tilted and its orbit is not perfectly circular. This is why longitude alone is not a complete correction.
What this can change in a BaZi chart
BaZi divides the day into twelve two-hour branches. Correcting a recorded birth time matters when the result crosses one of those boundaries—for example, when 15:02 civil time becomes 14:47 solar time.
That does not mean every chart changes. A birth well inside a two-hour block normally keeps the same hour branch. The useful output is therefore not merely a corrected time, but a receipt showing whether a boundary was crossed.
Use the free True Solar Time BaZi Calculator to apply the corrected time to a complete chart. For exact branch cutovers, read the BaZi hour-pillar boundary guide.
If two tools still disagree, follow the BaZi calculator difference audit from original civil input through timezone, solar correction, boundary rule and the first pillar that changes.
How Pillarwise calculates it
The production calculation uses:
- the selected city’s coordinates;
- the IANA Time Zone Database for the historical civil offset;
- Astronomy Engine to derive the Sun’s apparent hour angle and equation of time;
- the same deterministic resolver used by the Pillarwise chart engine.
You can compare the astronomical concepts with the official NOAA Solar Calculator. Pillarwise additionally exposes the timezone, longitude, equation-of-time and branch-boundary receipt used by the chart.
Limits and responsible use
City search uses city-center coordinates. For a very large municipality or a birth close to a branch boundary, exact coordinates and uncertainty in the recorded birth minute may matter. Historical timezone records can also contain political changes and local exceptions.
Treat boundary cases as uncertain inputs, not as false precision. If the recorded time itself is doubtful, start with birth-time correction before interpreting the hour pillar.
Core city matrix
True solar time by city
These are reviewed location pages, not automatic keyword variants. Every page opens a working city preset and documents two receipts produced by the same deterministic resolver as the main calculator.
United States
Los Angeles
America/Los_AngelesAlmost aligned with noon in January; the July result sits just after an hour-branch boundary.
- January · UTC−08:00
- 12:00 → 11:57:30
- July · UTC−07:00
- 12:00 → 11:00:58
Chicago
America/ChicagoThe longitude and equation-of-time terms nearly cancel at noon in the January example.
- January · UTC−06:00
- 12:00 → 11:59:54
- July · UTC−05:00
- 12:00 → 11:03:21
Houston
America/ChicagoWell west of the Central reference meridian, with a pronounced negative summer correction.
- January · UTC−06:00
- 12:00 → 11:29:03
- July · UTC−05:00
- 12:00 → 10:32:30
Phoenix
America/PhoenixThe 2026 examples keep UTC−07:00 in both seasons, isolating the seasonal equation-of-time change.
- January · UTC−07:00
- 12:00 → 11:22:12
- July · UTC−07:00
- 12:00 → 11:25:39
San Francisco
America/Los_AngelesWest of the Pacific reference meridian; the July noon example crosses into the preceding branch.
- January · UTC−08:00
- 12:00 → 11:40:48
- July · UTC−07:00
- 12:00 → 10:44:16
Seattle
America/Los_AngelesIts longitude is close to San Francisco, so the clock correction is similar despite the latitude gap.
- January · UTC−08:00
- 12:00 → 11:41:09
- July · UTC−07:00
- 12:00 → 10:44:37
Miami
America/New_YorkWest of the Eastern reference meridian, so daylight time pushes July apparent noon much earlier.
- January · UTC−05:00
- 12:00 → 11:29:45
- July · UTC−04:00
- 12:00 → 10:33:11
Boston
America/New_YorkEast of the Eastern standard meridian; the January longitude term outweighs the equation of time.
- January · UTC−05:00
- 12:00 → 12:06:17
- July · UTC−04:00
- 12:00 → 11:09:43
Canada
Toronto
America/TorontoWest of the Eastern reference meridian in both examples, with the larger gap under daylight time.
- January · UTC−05:00
- 12:00 → 11:32:56
- July · UTC−04:00
- 12:00 → 10:36:22
Vancouver
America/VancouverFarther west than the Pacific reference meridian, producing a clear summer hour-branch shift at noon.
- January · UTC−08:00
- 12:00 → 11:38:00
- July · UTC−07:00
- 12:00 → 10:41:28
Calgary
America/EdmontonWell west of the Mountain reference meridian; it has the largest July correction in this release set.
- January · UTC−07:00
- 12:00 → 11:14:09
- July · UTC−06:00
- 12:00 → 10:17:37
Ottawa
America/TorontoClose to the Eastern standard meridian, making the January receipt a clean equation-of-time example.
- January · UTC−05:00
- 12:00 → 11:47:44
- July · UTC−04:00
- 12:00 → 10:51:10
United Kingdom
London
Europe/LondonAlmost on Greenwich; the January gap is mostly equation of time, while July includes British Summer Time.
- January · UTC+00:00
- 12:00 → 11:50:05
- July · UTC+01:00
- 12:00 → 10:53:28
Manchester
Europe/LondonWest of Greenwich, adding about nine negative longitude minutes before the seasonal term in January.
- January · UTC+00:00
- 12:00 → 11:41:39
- July · UTC+01:00
- 12:00 → 10:45:02
Birmingham
Europe/LondonIts west-of-Greenwich longitude adds a modest negative term before the one-hour summer-clock shift.
- January · UTC+00:00
- 12:00 → 11:43:00
- July · UTC+01:00
- 12:00 → 10:46:23
Questions
Frequently asked
How do I calculate my true solar time right now?
Use the device-time button to fill the current local date and clock reading, then select the place where that reading applies. The calculator resolves that place's historical UTC offset and longitude before adding the date-specific equation of time.
Is true solar time the same as true sun time?
Usually, yes. True sun time is an informal name for local apparent solar time: time based on the actual Sun crossing the local meridian. It is distinct from uniform local mean solar time.
How is solar time different from clock time?
Clock time is uniform across an entire timezone; solar time varies continuously with longitude and season. The two agree only near the timezone's reference meridian, on dates when the equation of time is near zero.
What is the equation of time?
The seasonal difference between sundial time and mean clock time, caused by Earth's tilted axis and elliptical orbit. It swings between roughly −14 and +16 minutes over the year.
Does daylight saving time affect true solar time?
Yes. Civil clock time must first be interpreted with the historical UTC offset in force for that place and date. The longitude and equation-of-time corrections are then applied to the resulting instant.
Can true solar time fall on another date?
Yes. A sufficiently large correction near midnight can move the local apparent solar time to the previous or next calendar date.
Can true solar time change a BaZi chart?
It can change the hour pillar when corrected time crosses one of the two-hour branch boundaries. Most births well inside a branch keep the same hour pillar.
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