Local Sidereal Time (LST), Sidereal Day & Celestial Hour Angle (HA = LST − RA) Calculator

Compute Local Sidereal Time (LST), Local Hour Angle (HA), and time until meridian transit.

Local Sidereal Time (LST)
9.5 sidereal hrs
Target Local Hour Angle (HA = LST − RA) 1.25 hours
Target Hour Angle in Degrees (15°/hr) 18.75 degrees
Length of 1 Mean Sidereal Day (Solar Hours) 23.934 solar hrs
Inputs
⚡ Scenarios:
h GMST
Greenwich Mean Sidereal Time (GMST) in decimal hours (0.00 to 24.00 h).
° lon
Observer longitude in degrees (+East / −West).
h RA
Celestial object Right Ascension (RA) in decimal hours (0.00 to 24.00 h).
Results & Graph
Local Sidereal Time (LST)
9.5 sidereal hrs
Target Local Hour Angle (HA = LST − RA)
1.25 hours
Target Hour Angle in Degrees (15°/hr)
18.75 degrees
Length of 1 Mean Sidereal Day (Solar Hours)
23.934 solar hrs

Local Sidereal Time (LST)

Graph 1 • Sidereal Time & Hour Angle • Domain Architecture & Live Telemetry Maps Gmst Decimal Hours, Observer Longitude Deg, Target Right Ascension Hours through Sidereal Time & Hour Angle Formula.
ASTRONOMICAL & CELESTIAL T Local Sidereal Time (LST) 9.5 sidereal hrs Target Local Hour Angle (H 1.25 hours Sidereal Time & Hour Angle • Component Waterfall Local Sidereal Time (LST) 9.5 sidereal hrs Target Local Hour Angle (HA = 1.25 hours Target Hour Angle in Degrees ( 18.75 degrees Length of 1 Mean Sidereal Day 23.934 solar hrs
Graph 2 • Local Sidereal Time (LST) Across Gmst Decimal Hours Sweep (40% → 160%) Evaluates LST_hours = (GMST_hours + Longitude_deg / 15) mod 24; HourAngle = LST_ across 7 operating points (current input highlighted).
0 sidere 10.01 sidere 20.02 sidere 0.800 5.80 3.70 8.70 6.60 11.60 9.50 14.50 12.40 17.40 15.30 20.30 18.20 23.20
Graph 3 • Joint Sensitivity: Gmst Decimal Hours × Observer Longitude Deg Compares Local Sidereal Time (LST) when Observer Longitude Deg is shifted +25% (solid) vs. −25% (dashed).
0 sidere 8.30 sidere 16.61 sidere --- Observer Longitude Deg @ 75% 3.90 -30% 6.07 -15% 8.25 +0% 10.42 +15% 12.60 +30%
Summary: At GMST 14.5 h and longitude -75°, Local Sidereal Time is 9.5 h, placing target RA 8.25 h at a Local Hour Angle of 1.25 h (West of meridian / setting).
Summary: At GMST 14.5 h and longitude -75°, Local Sidereal Time is 9.5 h, placing target RA 8.25 h at a Local Hour Angle of 1.25 h (West of meridian / setting).
⚡ Send result to: Unit Converter →Scientific →Date Difference →
Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Sidereal Time & Hour Angle Formula

LSThours = (GMSThours + Longitudedeg / 15) mod 24
HourAngle = LSThours − RightAscensionhours
LST_hours = (GMST_hours + Longitude_deg / 15) mod 24; HourAngle = LST_hours − RightAscension_hours
  • gmstDecimalHours: Greenwich Mean Sidereal Time (GMST) in decimal hours (0.00 to 24.00 h).
  • observerLongitudeDeg: Observer longitude in degrees (+East / −West).
  • targetRightAscensionHours: Celestial object Right Ascension (RA) in decimal hours (0.00 to 24.00 h).

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

Worked Example: Sidereal Time & Hour Angle Worked Example

Compute Local Sidereal Time (LST), Local Hour Angle (HA), and time until meridian transit.

  1. Enter the input measurement, system configuration, or astronomical parameter.
  2. Apply the standard conversion or analytical equation: LST_hours = (GMST_hours + Longitude_deg / 15) mod 24; HourAngle = LST_hours − RightAscension_hours.
  3. Inspect the primary metric, secondary equivalents, and 3 real-time SVG graphs.
Result: Computes Sidereal Time & Hour Angle via LST_hours = (GMST_hours + Longitude_deg / 15) mod 24; HourAngle = LST_hours − RightAscension_hours.

Frequently Asked Questions

How does the Local Sidereal Time (LST), Sidereal Day & Celestial Hour Angle (HA = LST − RA) Calculator perform the calculation?

It evaluates LST_hours = (GMST_hours + Longitude_deg / 15) mod 24; HourAngle = LST_hours − RightAscension_hours 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

Local Sidereal Time (LST), Sidereal Day & Celestial Hour Angle (HA = LST − RA) Calculator: inputs, method, and how to read the result

Compute Local Sidereal Time (LST), Local Hour Angle (HA), and time until meridian transit.

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.

  • Gmst Decimal Hours: Greenwich Mean Sidereal Time (GMST) in decimal hours (0.00 to 24.00 h).
  • Observer Longitude Deg: Observer longitude in degrees (+East / −West).
  • Target Right Ascension Hours: Celestial object Right Ascension (RA) in decimal hours (0.00 to 24.00 h).

What the calculation includes

With the default values shown, Local Sidereal Time (LST) is 9.5 sidereal hrs. The calculation follows Sidereal Time & Hour Angle Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Gmst Decimal Hours from 14.5 h GMST to 15.95 h GMST changes Local Sidereal Time (LST) from 9.5 sidereal hrs to 10.95 sidereal hrs. 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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