Satellite Footprint Calculator
Calculate the coverage footprint radius, central earth angle, surface area, and maximum slant range for any satellite altitude and elevation mask.
2
Inputs
Live
Math
3
Related
Enter parameters and click Calculate to view results
Formula & Theory
ψ = arccos[(Rₑ / (Rₑ + h)) × cos(θ)] - θ, Footprint Radius = Rₑ × ψ, Area = 2πRₑ²(1 - cos ψ)This formula is used to calculate antenna parameters for satellite footprint calculator.
Overview
This satellite footprint calculator computes the maximum Earth surface coverage radius, central Earth angle, footprint area, and edge-of-coverage slant range for a satellite at any altitude and elevation mask. It is built for constellation planners, RF coverage engineers, HAM satellite operators, and students comparing how footprint size scales across LEO, MEO, and GEO orbits, and how many satellites are needed for continuous global or regional coverage.
Input Guide
Enter Satellite Altitude, Minimum Elevation Mask Angle exactly in the units shown by this satellite footprint. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Satellite Altitude — use km.
- Minimum Elevation Mask Angle — use °.
Output Guide
The results describe the calculated satellite footprint values for the inputs you entered. Check each value against the available space, selected components, feed system, and operating conditions before making a final design decision.
How This Calculator Works
The Satellite Footprint uses ψ = arccos[(Rₑ / (Rₑ + h)) × cos(θ)] - θ, Footprint Radius = Rₑ × ψ, Area = 2πRₑ²(1 - cos ψ). Supply Satellite Altitude (km), Minimum Elevation Mask Angle (°) in the displayed units, then use the calculated values as the first engineering target for this satellite communication design or analysis.
Design Notes
Setting the elevation mask to 0° models the theoretical geometric horizon — the absolute maximum footprint a satellite can ever illuminate, where the signal path grazes tangent to Earth's surface. Real systems never operate at this limit: applying a practical mask of 5°–10° accounts for the fact that ground antennas need clearance from terrain, buildings, and the worst atmospheric attenuation near the horizon. Comparing the 0° footprint against a 10° masked footprint for the same altitude shows exactly how much usable coverage is sacrificed for link reliability — often a meaningful percentage of the theoretical maximum.
Build and Tuning Notes
For constellation design, the footprint area at your chosen elevation mask directly determines how many satellites are needed for global or regional coverage: divide total target surface area by the single-satellite footprint area (with overlap margin) to get a first-order satellite count estimate. At GEO altitude, a single satellite's theoretical footprint spans nearly half the globe, which is why just three well-spaced GEO satellites can provide near-global coverage excluding the poles — but LEO constellations providing similar service need dozens to hundreds of satellites because each footprint is tiny and satellites move relative to the ground. Always re-run this calculation at your intended operational elevation mask, not 0°, before sizing a real constellation.
Frequently Asked Questions
What is the maximum Earth surface area a GEO satellite can cover?
A single geostationary satellite at 35,786 km altitude has a theoretical maximum central angle of about 81.3° measured at 0° elevation, corresponding to roughly 42% of Earth's total surface area. In practice this usable footprint shrinks once a realistic elevation mask is applied for ground station link quality.
Why does an elevation mask shrink the satellite footprint?
Ground receivers need a minimum angle above the local horizon, typically 5° to 15°, to avoid excessive atmospheric path length, terrain blockage, and multipath interference. Raising this elevation mask angle reduces the maximum central angle at which the satellite is considered usable, which directly shrinks both the footprint radius and the covered surface area compared to the theoretical 0° horizon case.
What is the sub-satellite point, and how does it relate to the footprint?
The sub-satellite point is the location directly beneath the satellite on Earth's surface, where the elevation angle as seen from the ground is exactly 90° (straight up) and slant range is at its minimum. The footprint radius calculated here represents how far outward from that central point the satellite remains visible above your chosen elevation mask.
How is footprint size used to plan a satellite constellation?
Constellation designers use single-satellite footprint area, combined with a desired overlap factor for continuity as satellites move, to estimate the total number of satellites needed for a coverage goal. Because footprint size shrinks sharply at lower altitudes, LEO constellations require far more satellites for the same coverage target than a MEO or GEO system, which is one of the central engineering tradeoffs in orbit selection.
Alex Warren
B.Sc. in Electrical & Electronic Engineering (EEE)
Alex specialises in antenna design and wave propagation. His expertise helps ensure these calculators present practical RF concepts, useful design estimates, and clear engineering guidance for students, HAM operators, and wireless professionals.