Astronomical Equation of Time (Δt Minutes), Sundial Offset & Apparent Solar Noon Calculator

Compute the Equation of Time (EoT minutes) and exact clock time of Local Apparent Solar Noon.

Equation of Time (Sundial − Clock)
15.552 minutes
Longitude Offset from TZ Meridian 56 minutes
Local Apparent Solar Noon (Decimal Hours) 12.674 hours
Total Sundial-to-Clock Correction 40.448 minutes
Inputs
⚡ Scenarios:
day N
Day of the year N (1 = Jan 1, 172 = Jun 21, 292 = Oct 19, 355 = Dec 21).
° lon
Observer longitude in degrees (+East / −West; e.g., NYC = −74.0°, London = −0.1°, Delhi = +77.2°).
UTC hrs
Local standard or daylight time zone offset from UTC in hours (e.g., −4 EDT, +5.5 IST).
Results & Graph
Equation of Time (Sundial − Clock)
15.552 minutes
Longitude Offset from TZ Meridian
56 minutes
Local Apparent Solar Noon (Decimal Hours)
12.674 hours
Total Sundial-to-Clock Correction
40.448 minutes

Equation of Time (Sundial − Clock)

Graph 1 • Equation of Time & Solar Noon • Domain Architecture & Live Telemetry Maps Ordinal Day Of Year1to365, Observer Longitude Degrees, Utc Time Zone Offset Hours through Equation of Time & Solar Noon Formula.
Equation of Time & Solar Noon • Generation → Conversion → Storage Bus 1. SOURCE / ARRAY 292 day N Ordinal Day Of Year1to 2. DELIVERED RATING 15.552 minutes Equation of Time (Sundia 3. SECONDARY OUTPUT 56 minutes Longitude Offset from TZ
Graph 2 • Equation of Time (Sundial − Clock) Across Ordinal Day Of Year1to365 Sweep (40% → 160%) Evaluates B = 360° × (N − 81) / 365; EoT_min = 9.87·sin(2B) − 7.53·cos(B) − 1.5· across 7 operating points (current input highlighted).
-3.71 minute 6.70 minute 17.11 minute 2.33 116.8day N -2.08 175.2day N -2.54 233.6day N 15.55 292day N 3.72 350.4day N -3.71 408.8day N -3.71 467.2day N
Graph 3 • Joint Sensitivity: Ordinal Day Of Year1to365 × Observer Longitude Degrees Compares Equation of Time (Sundial − Clock) when Observer Longitude Degrees is shifted +25% (solid) vs. −25% (dashed).
-6.13 minute 5.49 minute 17.11 minute --- Observer Longitude Degrees @ 75% -6.13 -30% 1.85 -15% 15.55 +0% 9.75 +15% -3.71 +30%
Summary: On Day 292, the Equation of Time is +15.55 minutes and longitude offset is 56 min, placing Local Apparent Solar Noon at 12:40 local clock time.
Summary: On Day 292, the Equation of Time is +15.55 minutes and longitude offset is 56 min, placing Local Apparent Solar Noon at 12:40 local clock time.
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Formula & Mathematical Methodology: Equation of Time & Solar Noon Formula

B = 360° × (N − 81) / 365
EoTmin = 9.87·sin(2B) − 7.53·cos(B) − 1.5·sin(B)
SolarNoon = 12:00 − (EoT / 60) + (TZMeridian − Longitude)/15
B = 360° × (N − 81) / 365; EoT_min = 9.87·sin(2B) − 7.53·cos(B) − 1.5·sin(B); SolarNoon = 12:00 − (EoT / 60) + (TZ_Meridian − Longitude)/15
  • ordinalDayOfYear1to365: Day of the year N (1 = Jan 1, 172 = Jun 21, 292 = Oct 19, 355 = Dec 21).
  • observerLongitudeDegrees: Observer longitude in degrees (+East / −West; e.g., NYC = −74.0°, London = −0.1°, Delhi = +77.2°).
  • utcTimeZoneOffsetHours: Local standard or daylight time zone offset from UTC in hours (e.g., −4 EDT, +5.5 IST).

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Equation of Time & Solar Noon Worked Example

Compute the Equation of Time (EoT minutes) and exact clock time of Local Apparent Solar Noon.

  1. Enter the input measurement, system configuration, or astronomical parameter.
  2. Apply the standard conversion or analytical equation: B = 360° × (N − 81) / 365; EoT_min = 9.87·sin(2B) − 7.53·cos(B) − 1.5·sin(B); SolarNoon = 12:00 − (EoT / 60) + (TZ_Meridian − Longitude)/15.
  3. Inspect the primary metric, secondary equivalents, and 3 real-time SVG graphs.
Result: Computes Equation of Time & Solar Noon via B = 360° × (N − 81) / 365; EoT_min = 9.87·sin(2B) − 7.53·cos(B) − 1.5·sin(B); SolarNoon = 12:00 − (EoT / 60) + (TZ_Meridian − Longitude)/15.

Frequently Asked Questions

How does the Astronomical Equation of Time (Δt Minutes), Sundial Offset & Apparent Solar Noon Calculator perform the calculation?

It evaluates B = 360° × (N − 81) / 365; EoT_min = 9.87·sin(2B) − 7.53·cos(B) − 1.5·sin(B); SolarNoon = 12:00 − (EoT / 60) + (TZ_Meridian − Longitude)/15 directly in your browser and renders three custom SVG charts in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this tool work offline?

Yes. All calculations run 100% locally in your browser with full offline PWA support.

Dates & Time · Astronomical & Celestial Time

Astronomical Equation of Time (Δt Minutes), Sundial Offset & Apparent Solar Noon Calculator: inputs, method, and how to read the result

Compute the Equation of Time (EoT minutes) and exact clock time of Local Apparent Solar Noon.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Ordinal Day Of Year1to365: Day of the year N (1 = Jan 1, 172 = Jun 21, 292 = Oct 19, 355 = Dec 21).
  • Observer Longitude Degrees: Observer longitude in degrees (+East / −West; e.g., NYC = −74.0°, London = −0.1°, Delhi = +77.2°).
  • Utc Time Zone Offset Hours: Local standard or daylight time zone offset from UTC in hours (e.g., −4 EDT, +5.5 IST).

What the calculation includes

With the default values shown, Equation of Time (Sundial − Clock) is 15.552 minutes. The calculation follows Equation of Time & Solar Noon Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Ordinal Day Of Year1to365 from 292 day N to 321 day N changes Equation of Time (Sundial − Clock) from 15.552 minutes to 14.443 minutes. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses official NIST Special Publication 811, IEEE/RFC systems engineering, APA psychometric, and USNO astronomical formulas.
  • Empirical metallurgy and calendar conversions represent standard reference-condition approximations.

Scope: Global NIST, IEEE, APA & Astronomical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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