{"id":3302,"date":"2026-02-21T18:00:00","date_gmt":"2026-02-21T18:00:00","guid":{"rendered":"https:\/\/pirhome.com\/?p=3302"},"modified":"2026-02-21T18:00:00","modified_gmt":"2026-02-21T18:00:00","slug":"pir-field-of-view-calculations","status":"publish","type":"post","link":"https:\/\/www.pirhome.com\/?p=3302","title":{"rendered":"Understanding PIR Sensor Field of View Calculations"},"content":{"rendered":"<h2>Introduction<\/h2>\n<p>To properly place a PIR sensor, you need to understand its field of view (FOV) and how it translates to actual coverage area. This article provides the formulas and calculations needed.<\/p>\n<h2>Basic Parameters<\/h2>\n<ul>\n<li><strong>Horizontal FOV (\u03b8_h):<\/strong> The angle the sensor covers side-to-side (typically 90-180\u00b0).<\/li>\n<li><strong>Vertical FOV (\u03b8_v):<\/strong> The angle top-to-bottom (typically 60-90\u00b0).<\/li>\n<li><strong>Mounting Height (H):<\/strong> Distance from sensor to floor.<\/li>\n<li><strong>Tilt Angle (\u03b1):<\/strong> Angle sensor is aimed downward from horizontal (0\u00b0 = straight ahead, 90\u00b0 = straight down).<\/li>\n<li><strong>Maximum Range (R_max):<\/strong> The farthest distance the sensor can detect (specified by manufacturer).<\/li>\n<\/ul>\n<h2>Coverage Area Geometry<\/h2>\n<p>The sensor&#8217;s detection pattern is roughly conical or pyramidal. The actual coverage on the floor depends on mounting height and tilt.<\/p>\n<h3>For Wall-Mounted Sensor (Typical)<\/h3>\n<p>The detection pattern projects onto the floor as a truncated sector. Key distances:<\/p>\n<ul>\n<li><strong>Near Limit (D_near):<\/strong> The closest point on the floor that is detected.<\/li>\n<li><strong>Far Limit (D_far):<\/strong> The farthest point detected (limited by range).<\/li>\n<li><strong>Width at distance D:<\/strong> W(D) = 2 \u00d7 D \u00d7 tan(\u03b8_h\/2).<\/li>\n<\/ul>\n<h2>Calculations<\/h2>\n<h3>Near Limit Calculation<\/h3>\n<p>For a sensor mounted at height H, tilted downward by angle \u03b1, the near limit is:<\/p>\n<p><strong>D_near = H \u00d7 tan(90\u00b0 &#8211; \u03b1 &#8211; \u03b8_v\/2)<\/strong> (if result is negative, coverage starts at the wall).<\/p>\n<h3>Far Limit Calculation<\/h3>\n<p>The far limit is the smaller of:<\/p>\n<ul>\n<li>R_max (sensor&#8217;s maximum range)<\/li>\n<li>Distance to where the top of the vertical FOV hits the floor: <strong>D_top = H \u00d7 tan(90\u00b0 &#8211; \u03b1 + \u03b8_v\/2)<\/strong><\/li>\n<\/ul>\n<h3>Example Calculation<\/h3>\n<p><strong>Given:<\/strong> H = 2.5m, \u03b8_v = 80\u00b0, \u03b1 = 20\u00b0, \u03b8_h = 100\u00b0, R_max = 10m.<\/p>\n<ol>\n<li>D_near = 2.5 \u00d7 tan(90\u00b0 &#8211; 20\u00b0 &#8211; 40\u00b0) = 2.5 \u00d7 tan(30\u00b0) = 2.5 \u00d7 0.577 = 1.44m.<\/li>\n<li>D_top = 2.5 \u00d7 tan(90\u00b0 &#8211; 20\u00b0 + 40\u00b0) = 2.5 \u00d7 tan(110\u00b0) = 2.5 \u00d7 (-2.747) negative \u2192 no top floor intersection, so far limit is R_max = 10m.<\/li>\n<li>Width at 5m: W = 2 \u00d7 5 \u00d7 tan(50\u00b0) = 10 \u00d7 1.192 = 11.92m.<\/li>\n<\/ol>\n<h2>Coverage Maps<\/h2>\n<p>For precise work, you can generate a coverage map by calculating the detection boundaries at various distances. This helps identify blind spots.<\/p>\n<h2>Ceiling-Mounted Sensors (360\u00b0)<\/h2>\n<p>For ceiling-mounted sensors, coverage is typically circular:<\/p>\n<ul>\n<li><strong>Radius:<\/strong> r = H \u00d7 tan(\u03b8\/2) where \u03b8 is the total coverage angle (often 90-110\u00b0).<\/li>\n<li><strong>Example:<\/strong> H = 3m, \u03b8 = 100\u00b0, r = 3 \u00d7 tan(50\u00b0) = 3 \u00d7 1.192 = 3.58m. Coverage diameter \u2248 7.2m.<\/li>\n<\/ul>\n<h2>Lens Effects<\/h2>\n<p>Note that the Fresnel lens creates discrete detection zones, not a continuous field. The above calculations give the <em>envelope<\/em> within which zones exist. Actual detection may have gaps.<\/p>\n<h2>Software Tools<\/h2>\n<p>Several manufacturers provide coverage calculation tools:<\/p>\n<ul>\n<li>Panasonic: PaPIRs Sensor Selection Tool<\/li>\n<li>Bosch: Detector Coverage Tool<\/li>\n<li>Honeywell: Coverage Calculator<\/li>\n<\/ul>\n<h2>Conclusion<\/h2>\n<p>Understanding FOV calculations ensures you place sensors correctly, avoiding blind spots and maximizing coverage efficiency.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction To properly place a PIR sensor, you need to understand its field of view (FOV) and how it translates to actual coverage area. This article provides the formulas and calculations needed. Basic Parameters Horizontal FOV (\u03b8_h): The angle the sensor covers side-to-side (typically 90-180\u00b0). Vertical FOV (\u03b8_v): The angle top-to-bottom (typically 60-90\u00b0). Mounting Height [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-3302","post","type-post","status-publish","format-standard","hentry","category-reference"],"blocksy_meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\r\n<title>Understanding PIR Sensor Field of View Calculations - PIRHOME<\/title>\r\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\r\n<link rel=\"canonical\" href=\"http:\/\/www.pirhome.com\/?p=3302\" \/>\r\n<meta property=\"og:locale\" content=\"en_US\" \/>\r\n<meta property=\"og:type\" content=\"article\" \/>\r\n<meta property=\"og:title\" content=\"Understanding PIR Sensor Field of View Calculations - PIRHOME\" \/>\r\n<meta property=\"og:description\" content=\"Introduction To properly place a PIR sensor, you need to understand its field of view (FOV) and how it translates to actual coverage area. 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