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Mean Solar Time Calculator

Calculate Local Mean Solar Time (LMST) and Greenwich Mean Solar Time (GMST). Mean solar time uses a fictitious mean sun that moves uniformly along the celestial equator.

Mean Solar Time

UTC / GMST

06:36:15.00

Greenwich Mean Solar Time

LMST

06:36:15.00

Local Mean Solar Time

Civil Time

06:36:15.00

Standard Time Zone (UTC+0)

LMST - Civil

0.00 min

Difference from zone time

Time Parameters

Standard Meridian

0 deg

Longitude Time Offset

0.0000 hours

Solar/Sidereal Ratio

1.00273791

Day Length Comparison

Mean Solar Day

24:00:00.000

86,400 SI seconds (by definition)

Sidereal Day

23:56:04.091

Rotation relative to stars

Difference

3:55.909

Solar day is longer

About Mean Solar Time

Mean Solar Time is based on a fictitious "mean sun" that moves uniformly along the celestial equator at a constant rate. Unlike apparent solar time (sundial time), mean solar time does not vary throughout the year. The difference between mean and apparent solar time is the Equation of Time. Modern civil time is based on mean solar time, with UTC serving as the global reference.

What Is Mean Solar Time?

Mean Solar Time (MST) is a timekeeping system based on a hypothetical "mean sun" that moves at a constant rate along the celestial equator, completing exactly one revolution per day. This is in contrast to Apparent Solar Time — the actual position of the real Sun in the sky, which varies in speed throughout the year due to Earth's elliptical orbit and axial tilt.

The difference between Apparent Solar Time and Mean Solar Time is the Equation of Time, which ranges from about +16 minutes to −14 minutes throughout the year. A sundial shows Apparent Solar Time; a clock shows Mean Solar Time. Before mechanical clocks became precise enough to track mean time, sundials were the only available timekeeping tool, and the Equation of Time correction was applied manually by astronomers and navigators.

The formula is simple: Local Mean Solar Time = UTC + (longitude / 15 hours). Each degree of longitude corresponds to exactly 4 minutes of time (since 360° / 24 hours = 15°/hour). This makes LMST the pure astronomical time at any location, independent of political time zone boundaries. Greenwich Mean Solar Time (GMST) is approximately equal to UT1 (Universal Time).

Local Mean Solar Time Formula

Mean solar time for any location is derived by adding the longitude offset (in time units) to UTC.

Local Mean Solar Time

LMST (hours) = UTC + longitude / 15

Where:

  • UTC= Coordinated Universal Time in decimal hours (e.g., 14:30 = 14.5)
  • longitude= Observer longitude in degrees (positive = east, negative = west)
  • 15= Degrees of longitude per hour of solar time (360° / 24h = 15°/h)
  • GMST= Greenwich Mean Solar Time — LMST at longitude 0°; approximately equal to UT1
  • solarNoon= When LMST = 12:00 — the local mean solar noon, differs from clock noon by Equation of Time

Clock Time vs. Solar Time

Modern clock time (your timezone) can differ from Local Mean Solar Time by a significant amount:

  • Timezone offset from UTC: Clocks are set to a standard meridian for the whole timezone (e.g., EST = UTC−5, based on 75°W). Locations east of 75°W are "ahead" of their clock noon; those west are "behind."
  • Longitude correction: New York (74°W) vs. timezone center (75°W) = 1° × 4 min/° = 4 minutes ahead of mean time. Denver (104.9°W) vs. MST center (105°W) = 0.1° × 4 min/° ≈ 0.4 minutes — very close.
  • Daylight Saving Time: Advances the clock by 1 hour, moving it 60 minutes away from solar time.

The total offset between clock time and Local Mean Solar Time can be as large as 90 minutes (western edge of a wide timezone in summer with DST).

How to Use This Calculator

  1. Enter UTC Time: Input the current UTC time in HH:MM:SS format (or click "Set Now" to use the current UTC time).
  2. Enter Longitude: Enter your observer longitude in decimal degrees. Positive = east (Europe, Asia, Africa); Negative = west (Americas, western Atlantic). Example: London = 0.0°; New York = −74.0°; Mumbai = 72.8°.
  3. Read Results: Local Mean Solar Time (LMST) and Greenwich Mean Solar Time (GMST = UT1) are displayed along with the number of hours LMST differs from UTC.

Applications

Astronomers use Local Mean Solar Time as the basis for transit observations — a star crosses the meridian (due south) when its Right Ascension equals the Local Sidereal Time, which is derived from LMST. Solar observers need LMST to predict when the Sun reaches its highest point (solar noon) and to plan meridian transit observations.

Solar energy engineers use mean solar time to predict daily solar position accurately. A solar tracker that targets peak energy production must calculate solar noon at the installation's specific longitude — which may differ significantly from local clock noon. The LMST calculation is the foundation of this.

Historians and archaeologists studying ancient monuments that align with celestial events (solstice sunrises, noon shadow alignments) use mean solar time to interpret these alignments, since historical societies used solar time rather than political timezones.

Worked Examples

LMST for London at 14:30 UTC

Problem:

What is Local Mean Solar Time in London (0.1°W) when UTC is 14:30?

Solution Steps:

  1. 1UTC = 14:30 = 14.5 hours
  2. 2Longitude = −0.1° (very slightly west of Greenwich)
  3. 3LMST = 14.5 + (−0.1)/15 = 14.5 − 0.00667 = 14.4933 hours
  4. 414.4933 hours = 14:29:36
  5. 5LMST ≈ 14:30 (almost identical to UTC — London is very close to the prime meridian)

Result:

London LMST at UTC 14:30 ≈ 14:29:36. Solar noon in London occurs at approximately UTC 12:00 (±Equation of Time).

LMST for New York

Problem:

What is LMST in New York (74°W) at UTC 17:00?

Solution Steps:

  1. 1UTC = 17:00 = 17.0 hours
  2. 2Longitude = −74.0° (west)
  3. 3LMST = 17.0 + (−74.0)/15 = 17.0 − 4.933 = 12.067 hours
  4. 412.067 hours ≈ 12:04
  5. 5So UTC 17:00 = LMST 12:04 in New York — close to solar noon

Result:

New York LMST at UTC 17:00 ≈ 12:04. Solar noon in New York is approximately 12:04 LMST (17:04 UTC ± Equation of Time).

Solar Noon Clock Time

Problem:

What clock time is solar noon in Chicago (87.6°W, CDT = UTC−5)?

Solution Steps:

  1. 1LMST noon = 12:00 → UTC noon at Chicago longitude = 12 − (−87.6/15) = 12 + 5.84 = 17:50 UTC
  2. 2CDT offset = UTC−5: clock time = 17:50 − 5:00 = 12:50 CDT
  3. 3Also subtract Equation of Time (varies by date, e.g., ~+3 min in early March)
  4. 4Solar noon in Chicago ≈ 12:47 PM CDT in early March

Result:

Solar noon in Chicago occurs around 12:50 PM CDT (before EoT correction), not at 12:00 PM.

Tips & Best Practices

  • ✓Divide your longitude by 15 to get your time offset from UTC in hours — e.g., 75°W / 15 = 5 hours behind UTC.
  • ✓Each degree of longitude = 4 minutes of solar time. If you're 10° east of your timezone center, solar noon is 40 minutes earlier than clock noon.
  • ✓Solar panels peak when LMST ≈ 12:00 (adjusted for Equation of Time) — not necessarily at clock noon.
  • ✓Ancient sundials show Apparent Solar Time, not Mean Solar Time — the Equation of Time correction was tabulated separately in almanacs.
  • ✓The formula LMST = UTC + lon/15 is the basis for all solar position calculations used in solar energy and astronomy.
  • ✓GMST at longitude 0° ≈ UT1 — the two differ by at most 0.9 seconds (the DUT1 value broadcast in time signals).

Related Calculators

Apparent Solar Time

Calculate the actual sundial time including Equation of Time

Equation of Time

Find the difference between sundial and clock time

Frequently Asked Questions

GMT originally referred to Greenwich Mean Solar Time — the mean solar time at the Royal Observatory in Greenwich. Since 1972, the term has become ambiguous: the UK uses GMT as a civil timezone equal to UTC (which is based on atomic clocks, not the Sun). Greenwich Mean Solar Time and UTC differ by up to 0.9 seconds (the DUT1 correction). For practical purposes, GMT, UTC, and GMST are all treated as equivalent in most non-astronomical contexts.
Solar noon (when the Sun crosses the meridian) differs from 12:00 clock time for two reasons: (1) your longitude may differ from your timezone's reference meridian, causing a fixed offset; (2) the Equation of Time — the difference between mean and apparent solar time — adds up to ±16 minutes of variation throughout the year. The combination of these two effects means solar noon can occur anywhere from about 11:30 AM to 12:45 PM depending on location, date, and DST status.
UT1 (Universal Time 1) is the modern incarnation of Greenwich Mean Solar Time, based on Earth's actual rotation angle (expressed as a time). It is continuously measured by radio telescopes tracking the positions of distant quasars. UTC is kept within 0.9 seconds of UT1 by inserting leap seconds. The difference UT1−UTC (called DUT1) is broadcast in time signals and is typically within ±0.2 seconds.
Mean Solar Time tracks the position of the mean Sun, which completes one revolution in 24 hours (the solar day). Sidereal Time tracks Earth's rotation relative to distant stars, which completes one revolution in about 23 hours 56 minutes (the sidereal day, about 4 minutes shorter). The difference arises because Earth has moved about 1° along its orbit during one rotation, so it must rotate an extra ~1° to bring the Sun back to the meridian. Sidereal time is used for telescope pointing; mean solar time for civil timekeeping.
This calculator gives Local Mean Solar Time, which gives you the approximate solar noon (when LMST = 12:00, the mean Sun is on the meridian). For the exact apparent solar noon (when the real Sun is highest), you need to also apply the Equation of Time correction for the specific date. Use the Equation of Time Calculator to find that correction, then add or subtract it from 12:00 LMST to get the apparent solar noon at your location.

Sources & References

Last updated: 2026-06-06

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Editorial Note

MyCalcBuddy Editorial Team

This page is maintained as an educational calculator reference.

Source

Formula Source: Standard Mathematical References

by Various

UpdatedLast reviewed: May 2026
CheckedFormula checks are based on standard references and internal QA review.

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