Grid Square Distance Calculator
Created by: Natalie Reed
Last updated:
Enter two sets of coordinates to get great-circle distance, forward and reciprocal bearings, long-path alternative, and auto-generated Maidenhead grid locators for both stations. Essential for VHF contests, POTA grid logging, and beam aiming.
Grid Square Distance Calculator
Amateur RadioCalculate the distance and bearing between any two amateur radio Maidenhead grid squares using the Haversine formula, and convert your lat/lon to a 6-character grid locator.
Note: These results are for guidance only and shouldn't be taken as professional advice. Always double-check with a qualified expert before making decisions.
What is a Grid Square Distance Calculator?
The Grid Square Distance Calculator computes the great-circle (shortest surface path) distance and forward bearing between any two geographic coordinates, converts both locations to 4-character and 6-character Maidenhead grid locators, and calculates the long-path alternative. It is the essential tool for amateur radio operators who need to know exactly how far away a station is, which direction to point a beam antenna, and whether the long path might offer better propagation than the short path.
Maidenhead grid squares are a hierarchical geographic reference system adopted by the amateur radio community at the 1980 VHF convention in Maidenhead, UK. The Earth's surface is divided into 18 × 18 fields identified by two letters (AA–RR), each subdivided into 10 × 10 numbered squares (00–99), yielding a 4-character locator (e.g., FN31) covering a 5° longitude × 2° latitude rectangle. Adding a two-letter sub-square suffix (e.g., FN31pr) gives a 6-character locator covering a 2.5' longitude × 1' latitude area — roughly 4 × 2 km at mid-latitudes.
Grid squares appear throughout amateur radio operating: VHF and UHF contests award multipliers for each unique grid worked; POTA and SOTA activators report their grid with every QSO; weak-signal digital modes like FT8 and JS8Call include the 4-character grid in every exchange as the sole location identifier; EME (Earth-Moon-Earth) operators use grid distance to calculate the approximate path geometry. Knowing your grid and the grid of the station you are working is fundamental to most modern amateur operating activities.
Beam antenna aiming requires knowing both the forward bearing (from your station to the target) and the reciprocal bearing (from the target back to you). If you are in FN31 near New York and the DX station is in IO91 near London, the short-path bearing from New York is approximately 50° (northeast). The reciprocal bearing the London station uses to beam back toward New York is 50° + 180° = 230° (southwest). This calculator provides both values directly, eliminating manual trigonometry when the bands open.
How the Grid Square Distance Calculator Works
Great-circle distance is computed using the Haversine formula, which is numerically stable for all distances including short paths and antipodal points. The formula first computes an intermediate value a = sin²(Δlat/2) + cos(lat1) × cos(lat2) × sin²(Δlon2), then derives the central angle c = 2 × atan2(√a, √(1−a)), and finally the distance d = R × c where R = 6371 km (mean Earth radius). The result is accurate to within 0.3% of the true geodetic distance, which is more than sufficient for antenna aiming and propagation planning.
Bearing from point 1 to point 2 uses the great-circle initial bearing formula: θ = atan2(sin(Δlon) × cos(lat2), cos(lat1) × sin(lat2) − sin(lat1) × cos(lat2) × cos(Δlon)), converted from radians to degrees and normalized to [0°, 360°] by adding 360° and taking mod 360°. This gives the true north bearing (compass bearing relative to geographic north, not magnetic north). For actual antenna aiming you must apply your local magnetic declination, which varies from −20° in parts of the US Pacific Northwest to +15° in New England.
The Maidenhead encoding algorithm proceeds in three tiers. For longitude: add 180° to shift to [0°, 360°]; field letter index = floor(adjusted_lon / 20); square digit = floor((adjusted_lon mod 20) / 2); sub-square letter index = floor(((adjusted_lon mod 20) mod 2) × 12). For latitude: add 90° to shift to [0°, 180°]; field letter index = floor(adjusted_lat / 10); square digit = floor(adjusted_lat mod 10); sub-square letter index = floor((adjusted_lat mod 1) × 24). Field letters use A–R; sub-square letters use a–x (lowercase by convention).
Haversine distance and bearing formulas
a = sin²(Δlat/2) + cos(lat1) × cos(lat2) × sin²(Δlon/2)
d = 2 × R × arcsin(√a), R = 6371 km
θ = atan2(sin(Δlon)×cos(lat2), cos(lat1)×sin(lat2) − sin(lat1)×cos(lat2)×cos(Δlon)) mod 360°
reciprocalBearing = (θ + 180°) mod 360°
longPathKm = 40075 − shortPathKm (circumference of Earth minus short path)
Maidenhead field: floor((lon+180)/20) → A–R; floor((lat+90)/10) → A–R
Maidenhead square: floor((lon+180)%20 / 2) → 0–9; floor((lat+90)%10) → 0–9
Example Calculations
New York (FN30) to London (IO91)
New York: lat 40.7°N, lon 74.0°W. London: lat 51.5°N, lon 0.1°W. Δlat = 10.8°, Δlon = 73.9°. Haversine gives d ≈ 5,567 km. Bearing from New York ≈ 51° (NE). Reciprocal ≈ 231° (SW). Long path ≈ 40,075 − 5,567 = 34,508 km at bearing 231° + 180° = 51° reversed, i.e., 231° from London goes the long way around at ≈231°.
Grid square area at 45°N vs equator
A 4-char Maidenhead square spans 5° longitude × 2° latitude. At the equator (0° lat): lon span = 5 × 111.32 km = 556.6 km; lat span = 2 × 111.32 km = 222.6 km; area ≈ 123,900 km². At 45°N: lon span = 5 × 111.32 × cos(45°) = 393.6 km; lat span unchanged 222.6 km; area ≈ 87,600 km² — about 29% smaller than the equatorial square.
VHF contest — grid distance scoring
Station in DM79 (Denver, CO, ~39°N 104°W) working station in FN31 (New Haven, CT, ~41°N 73°W). Haversine: Δlat = 2°, Δlon = 31°. d ≈ 2,642 km. In ARRL VHF contests on 2m, contacts over 300 km are worth 1 point per km for some categories — this single grid pair is worth ~2,642 points plus adds two new grids as multipliers.
Common Amateur Radio Uses
- Beam antenna aiming for DX contacts — compute forward bearing to target, then apply local magnetic declination for compass heading
- VHF and UHF grid square contest distance verification and multiplier planning
- POTA activator grid confirmation — verifying your 4-character grid before announcing on the spotting network
- Long-path propagation planning on 20m and 40m for contacts with Australia, Japan, and South America from North America
- SOTA and WWFF activator grid identification for summit-to-summit and park-to-park contacts
- EME (moonbounce) path geometry estimation — computing great-circle distance to verify both stations have similar antenna elevation angles during the contact window
Tips for Better Ham Radio Planning
Magnetic declination is the offset between true north (geographic north pole) and magnetic north (where a compass points). The Haversine formula and Maidenhead grid encoding both use true north bearings. For antenna rotator heading, you must convert: compassHeading = trueBearing − declination (positive declination = compass reads east of true). In Seattle (declination ≈ +15°E), pointing a beam at 30° true north requires setting the rotator to 30° − 15° = 15°. Declination values are available from the NOAA World Magnetic Model at ngdc.noaa.gov.
The long path is genuinely useful for trans-Pacific and trans-polar contacts when short-path propagation is blocked or degraded. Polar routes (short path from North America to Asia) are frequently absorbed by high-latitude auroral absorption during periods of elevated geomagnetic activity. During these events, the long path (routing the signal around the opposite side of the Earth through mid-latitudes and the southern hemisphere) may carry the signal with far lower absorption. If your short-path bearing to Japan from New York is 320° (NNW through the Arctic), the long path at 140° (SSE through the south Atlantic) avoids the polar absorption entirely.
For POTA activations, always verify your grid before and during the activation — not just at your home address. Many parks span multiple grid squares, and hunters who need specific grids will ask which grid you are physically operating from. A GPS or smartphone mapping app showing your decimal coordinates can be fed directly into this calculator to generate the correct 6-character Maidenhead locator at your exact position within the park. The POTA spotting network (pota.app) accepts both 4- and 6-character grids in the spot comments.
Frequently Asked Questions
What is a Maidenhead grid square?
The Maidenhead Locator System divides the Earth into a hierarchical grid used by amateur radio operators to identify locations. A 4-character locator (e.g., FN31) covers a 5° longitude × 2° latitude rectangle (about 200 × 222 km at mid-latitudes). A 6-character locator (e.g., FN31pr) adds a subsquare of 12.5' × 5' (about 23 × 9 km). Grid squares are widely used in VHF/UHF contests, POTA and SOTA logging, satellite contacts, and weak-signal digital modes.
How do I find my grid square?
Find your decimal latitude and longitude (from GPS, QRZ.com, or Google Maps), then enter it here — the calculator derives the 6-character grid. Alternatively, use an online Maidenhead converter or your logging software (Ham Radio Deluxe, N1MM+, WSJT-X all display your grid). Many modern transceivers with GPS also display the grid. For POTA, the park's grid is listed on the pota.app park database.
What is the long path and when do you use it?
Every great circle path has two arcs: the short path (the shorter route) and the long path (the longer arc, opposite direction). Long path = 40,075 km − short path. Long-path contacts are attempted when propagation over the short path is degraded (blocked by the polar region, propagating entirely through the sunlit ionosphere) but the long path has favorable dark-side conditions. 20m and 40m long-path contacts between Europe and Japan or Australia are common in the hours around gray-line.
Why does the same grid square cover different physical areas at different latitudes?
Maidenhead grid squares have fixed angular dimensions (2° lat × 5° lon for 4-char), but the physical size depends on latitude. At the equator, 1° longitude = 111 km; at 60°N, 1° longitude = 55 km. So a grid square in Scandinavia is physically about half the width of one in the Caribbean. The area shown in the calculator varies with the average latitude of the two stations.
How accurate is the Haversine formula for radio path calculations?
The Haversine formula gives great-circle distance accurate to within 0.3% of the true geodetic distance using the WGS84 ellipsoid model. For radio purposes (antenna aiming, propagation path calculation, POTA grid confirmation), this is more than adequate. Professional geodesy uses the Vincenty formula for higher accuracy on the WGS84 ellipsoid, but the difference at HF radio path scales is under 1 km even for antipodal paths.
How does POTA use grid squares?
Parks on the Air activators log their grid square with each QSO. Many POTA hunters track unique grids worked as a separate achievement alongside unique parks. A park in a rare or less-populated grid generates extra demand from hunters who need that square. The grid is typically the 4-character Maidenhead locator, though 6-character is sometimes used for contest logging. POTA activators announce their grid on the spotting network to attract grid-hungry chasers.
Sources and References
- ARRL Antenna Book, 24th Edition — propagation appendix including great-circle calculations (ARRL, 2011)
- John Davies G3YXM — "Amateur Radio Astronomy" grid locator section (RSGB, 2005)
- International Telecommunication Union — ITU-R M.1172 grid locator encoding specification
- Maidenhead Locator System — adopted at the VHF Convention, Maidenhead, UK (1980); documented by John Morris GM4ANB