Radio/Optical Horizon Formulas

NOTES: These formulae can be used (especially the optical variants) to estimate general questions, such as "how far away can I see Pike's Peak Mountain?". For that question; set the calculator to Optical Horizon, Feet and Statute Miles and use 3500 ft for sensor height (the height of the east slope approach to Pike's Peak) and 14,000 ft for target height (Pike's Peak Height). You'll get an answer of about 234.88 statute miles visibility for Pike's Peak.

Simplified Radar/Optical Horizon Formulas

SOURCE: Practical ESM Analysis by Sue Robertson

Where:

d: Radar/Optical Horizon Distance
h_sensor: Height of Sensor
h_target: Height of Target
C: Unit Coefficient

Known Unit Coefficients (C) are:

Radar Horizon

1.23 - Sensor Height in Feet, Distance to Radar Horizon in Nautical Miles.
4.124 - Sensor Height in Meters, Distance to Radar Horizon in Kilometers.
4124 - Sensor Height in Meters, Distance to Radar Horizon in Meters.

Optical Horizon

1.15 - Sensor Height in Feet, Distance to Optical Horizon in Nautical Miles.
1.323397 - Sensor Height in Feet, Distance to Optical Horizon in Statute Miles.
2.083 - Sensor Height in Meters, Distance to Optical Horizon in Nautical Miles.
3.8544 - Sensor Height in Meters, Distance to Optical Horizon in Kilometers.

Simplified Radio-Optical Horizon Calculator

Sensor Height
Target Height

Distance to Horizon

Pre-Calculated Radar Horizons (Nautical Miles)
Target Height	Sensor Height
Target Height	8 ft (2.43m) AGL (Vehicle Radars)	50 ft (15.24m) AGL (AN/SPY-1)	127.953 ft (39m) AGL (CLAM SHELL Mast)	500 ft (152.4m) AGL (Aerostat Balloon)	1,500 ft (457.2m) AGL	15,000 ft (4,562m) AGL)	32,000 ft (10 km) AGL (AWACS)
50 ft (15.24m)	12.18	17.39	22.61	36.20	56.34	159.34	228.73
500 ft (152.4m)	30.98	36.2	41.42	55.01	75.14	178.15	247.53
5,000 ft (1,524m)	51.5	95.67	100.89	114.48	134.61	237.62	307
15,000 ft (4,572m)	86.65	159.34	164.56	178.15	198.28	301.29	370.67
25,000 ft (7,620m)	110.85	203.18	208.39	221.98	242.12	345.12	414.51
50,000 ft (15,240m)	155.32	283.73	288.95	302.54	322.67	425.68	495.07
100,000 ft (30,480m)	218.22	397.66	402.87	416.46	436.60	539.60	608.99
328,000 ft (100 km) (Karman Line)	707.92	713.13	718.35	731.94	752.07	855.08	924.47
2,126,000 ft (648 km) (IRBM Apogee)	1796.92	1802.14	1807.35	1820.94	1841.08	1944.08	2013.47
5,383,000 ft (1640.7 km) (ICBM Apogee)	2857.24	2862.46	2867.67	2881.26	2901.4	3004.40	3073.79
NOTES: IRBM Apogee is for THOR, while ICBM apogee is for Minuteman I.

Pre-Calculated Radar Horizons (Kilometers)
Target Height	Sensor Height
Target Height	8 ft (2.43m) AGL (Vehicle Radars)	50 ft (15.24m) AGL (AN/SPY-1)	127.953 ft (39m) AGL (CLAM SHELL Mast)	500 ft (152.4m) AGL (Aerostat Balloon)	1,500 ft (457.2m) AGL	15,000 ft (4,562m) AGL)	32,000 ft (10 km) AGL (AWACS)
50 ft (15.24m)	22.56	32.21	41.87	67.04	104.34	295.10	423.61
500 ft (152.4m)	57.37	67.04	76.71	101.88	139.16	329.93	458.43
5,000 ft (1,524m)	95.38	177.18	186.85	212.02	249.30	440.07	568.56
15,000 ft (4,572m)	160.48	295.10	304.77	329.93	367.21	557.99	686.48
25,000 ft (7,620m)	205.29	376.29	385.94	411.11	448.41	639.16	767.67
50,000 ft (15,240m)	287.65	525.47	535.14	560.30	597.58	788.36	916.87
100,000 ft (30,480m)	404.14	736.47	746.12	771.28	808.58	999.34	1127.85
328,000 ft (100 km) (Karman Line)	1311.07	1320.72	1330.38	1355.55	1392.83	1583.61	1712.12
2,126,000 ft (648 km) (IRBM Apogee)	3327.90	3337.56	3347.21	3372.38	3409.68	3600.44	3728.95
5,383,000 ft (1640.7 km) (ICBM Apogee)	5291.61	5301.28	5310.92	5336.09	5373.39	5564.15	5692.66
NOTES: IRBM Apogee is for THOR, while ICBM apogee is for Minuteman I.

Extraterrestial Radar Horizon Formula

Where:

d: Distance to Radar Horizon (kilometers)
R: Planetary Radius (kilometers) (Earth is 6,378 km)
h_sensor: Height of Sensor (kilometers)
h_target: Height of Target (kilometers)

Extraterrestial Radar Horizon Calculator

Planetary Radius (kilometers)
Sensor Height (kilometers)
Target Height (kilometers)

Distance to Radar Horizon (kilometers)