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active-action="action-pagesabout"><i class="fa-duotone fa-user-tie color-about fa-fw"></i><p>关于</p></a><a href="https://www.travellings.cn/go-by-clouds.html" target="_blank" active-action="action-https:wwwtravellingscngo-by-cloudshtml" rel="external nofollow noopener noreferrer"><i class="fa-duotone fa-subway color-travellings fa-fw"></i><p>Travelling</p></a></div></div></div></div><div id="scroll-down" style="display:none"><i class="fa fa-chevron-down scroll-down-effects"></i></div></div></div><div id="safearea"><div class="body-wrapper"><div id="l_main" class=""><article itemscope="" itemtype="http://schema.org/Article" class="article post white-box reveal md shadow floatable blur article-type-post" id="post" itemprop="blogPost"><link itemprop="mainEntityOfPage" href="https://blog.mhuig.top/p/5e7ad437/"><span hidden="" itemprop="publisher" itemscope="" itemtype="http://schema.org/Organization"><meta itemprop="name" content="Magicland"></span><span hidden="" itemprop="post" itemscope="" itemtype="http://schema.org/CreativeWork"><meta itemprop="name" content="LBS 球面距离公式"><meta itemprop="description" content="详解LBS应用中的球面距离计算方案，推荐采用Haversine公式解决短距离计算时的舍入误差问题，提供Python实现代码：通过经纬度弧度转换、半正矢函数(hav)及地球半径(6371km)计算两点距离，附完整函数实现。"></span><span hidden=""><meta itemprop="image" content="/lib/favicon/android-chrome-192x192.png"></span><div class="article-meta" id="top"><h1 class="title" itemprop="name headline"> LBS 球面距离公式</h1><div class="new-meta-box"><div class="new-meta-item author" itemprop="author" itemscope="" itemtype="http://schema.org/Person"> <a itemprop="url" class="author" target="_blank" href="https://mhuig.top/" rel="nofollow noopener" alt="author"><img itemprop="image" src="/lib/avatar/avatar-16.webp" class="lazyload" data-srcset="/lib/avatar/avatar-16.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw=="><p itemprop="name">MHuiG</p></a></div><div class="new-meta-item wordcount"><a class="notlink"><i class="fa-duotone fa-keyboard fa-fw" aria-hidden="true"></i><p>字数：323 字</p></a></div><div class="new-meta-item readtime"><a class="notlink"><i class="fa-duotone fa-hourglass-half fa-fw" aria-hidden="true"></i><p>时长：1 分钟</p></a></div></div></div><div id="layoutHelper-page-plugins"></div><div id="post-body" itemprop="articleBody"><p>维基百科推荐使用 Haversine 公式，理由是 Great-circle distance 公式用到了大量余弦函数， 而两点间距离很短时（比如地球表面上相距几百米的两点），余弦函数会得出<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="7.425ex" height="1.557ex" role="img" focusable="false" viewBox="0 -666 3281.7 688"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="0.999…"><g data-mml-node="mn" data-latex=".999"><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z"></path><path data-c="2E" d="M192 53C192 82 168 106 139 106 110 106 86 82 86 53 86 24 110 0 139 0 168 0 192 24 192 53Z" transform="translate(500,0)"></path><path data-c="39" d="M116 140C83 140 67 123 67 89 67 14 128-22 207-22 287-22 351 18 398 99 437 166 457 243 457 329 457 456 434 546 388 599 349 644 304 666 253 666 194 666 145 645 106 602 63 557 42 503 42 440 42 379 60 327 96 284 134 238 183 215 242 215 294 215 334 243 361 299L361 286C361 177 342 103 303 63 272 30 239 14 206 14 166 14 137 23 118 42 149 42 165 60 165 91 165 119 144 140 116 140M243 246C204 246 175 266 155 306 144 329 138 374 138 439 138 504 145 548 158 573 180 613 212 633 253 633 294 633 324 608 343 558 354 531 361 485 361 420 361 333 322 246 243 246Z" transform="translate(778,0)"></path><path data-c="39" d="M116 140C83 140 67 123 67 89 67 14 128-22 207-22 287-22 351 18 398 99 437 166 457 243 457 329 457 456 434 546 388 599 349 644 304 666 253 666 194 666 145 645 106 602 63 557 42 503 42 440 42 379 60 327 96 284 134 238 183 215 242 215 294 215 334 243 361 299L361 286C361 177 342 103 303 63 272 30 239 14 206 14 166 14 137 23 118 42 149 42 165 60 165 91 165 119 144 140 116 140M243 246C204 246 175 266 155 306 144 329 138 374 138 439 138 504 145 548 158 573 180 613 212 633 253 633 294 633 324 608 343 558 354 531 361 485 361 420 361 333 322 246 243 246Z" transform="translate(1278,0)"></path><path data-c="39" d="M116 140C83 140 67 123 67 89 67 14 128-22 207-22 287-22 351 18 398 99 437 166 457 243 457 329 457 456 434 546 388 599 349 644 304 666 253 666 194 666 145 645 106 602 63 557 42 503 42 440 42 379 60 327 96 284 134 238 183 215 242 215 294 215 334 243 361 299L361 286C361 177 342 103 303 63 272 30 239 14 206 14 166 14 137 23 118 42 149 42 165 60 165 91 165 119 144 140 116 140M243 246C204 246 175 266 155 306 144 329 138 374 138 439 138 504 145 548 158 573 180 613 212 633 253 633 294 633 324 608 343 558 354 531 361 485 361 420 361 333 322 246 243 246Z" transform="translate(1778,0)"></path></g><g data-mml-node="mo" data-latex="…" transform="translate(2444.7,0)"><path data-c="2026" d="M751 53C751 83 725 106 695 106 664 106 638 83 638 53 638 23 664 0 695 0 725 0 751 23 751 53M475 53C475 83 449 106 419 106 388 106 363 83 363 53 363 23 388 0 419 0 449 0 475 23 475 53M200 53C200 83 174 106 143 106 113 106 87 83 87 53 87 23 113 0 143 0 173 0 200 23 200 53Z"></path></g></g></g></svg></mjx-container> 的结果， 会导致较大的舍入误差。而 Haversine 公式采用了正弦函数，即使距离很小，也能保持足够的有效数字。 以前采用三角函数表计算时的确会有这个问题，但经过实际验证，采用计算机来计算时，两个公式的区别不大。 稳妥起见，这里还是采用 Haversine 公式。</p><div class="story post-story"><h2 id="Haversine公式"><a href="#Haversine公式" class="headerlink" title="Haversine公式"></a>Haversine 公式</h2><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:73.729ex"><svg style="vertical-align:-1.785ex;min-width:73.729ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="4.701ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -1289)"><g data-mml-node="math" data-latex="
\text{haversin}(\frac{d}{R}) = \text{haversin}(\varphi_2 - \varphi_1) + \cos(\varphi_1) \cos(\varphi_2) \text{haversin}(\Delta\lambda)
"><g data-mml-node="mtable" data-latex="
\text{haversin}(\frac{d}{R}) = \text{haversin}(\varphi_2 - \varphi_1 ) + \cos(\varphi_1 ) \cos(\varphi_2 ) \text{haversin}(\Delta\lambda)
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data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(2)}"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 101 292L101 208C101 129 121 47 160-40 201-131 251-199 311-245 314-247 317-248 318-248Z"></path><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z" transform="translate(389,0)"></path><path data-c="29" d="M78-245C138-199 188-131 229-40 268 47 288 129 288 208L288 292C288 371 268 453 229 540 188 631 138 699 78 745 75 747 72 748 71 748 62 748 57 743 57 734 57 730 59 726 62 723 114 683 156 617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z" transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.05ex" xmlns="http://www.w3.org/2000/svg" width="1.717ex" height="1.595ex" role="img" focusable="false" viewBox="0 -683 759 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="R"><g data-mml-node="mi" data-latex="R"><path data-c="1D445" d="M739 531C739 582 713 621 662 649 621 672 572 683 517 683L235 683C212 683 202 682 202 659 202 652 205 647 211 646 221 645 229 644 234 644 264 643 281 641 286 640 291 639 294 636 294 631 294 629 293 623 290 613L158 82C153 60 143 46 128 41 121 39 103 38 72 38 50 38 41 37 41 15 41 4 47-1 59 0L183 3 309 0C325-1 333 8 333 23 333 33 322 38 301 38 261 38 241 43 241 52 241 52 242 54 244 68L308 327 423 327C492 327 527 298 527 241 527 232 522 210 513 174 502 132 497 104 497 89 497 13 556-22 632-22 660-22 687-9 714 16 741 41 755 68 755 96 755 106 750 111 739 111 732 111 726 106 723 95 712 64 698 41 682 28 666 15 651 8 636 8 613 8 601 27 601 64 601 88 604 125 611 176 614 197 615 212 615 223 615 276 587 315 531 339 625 362 739 429 739 531M609 616C629 603 639 581 639 550 639 530 635 507 626 480 599 398 531 357 422 357L316 357 379 610C384 631 392 642 403 643 408 644 428 644 463 644 528 644 566 642 609 616Z"></path></g></g></g></svg></mjx-container>为地球半径，可取平均值 6371.137km</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.493ex" xmlns="http://www.w3.org/2000/svg" width="2.467ex" height="1.493ex" role="img" focusable="false" viewBox="0 -442 1090.6 660"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\varphi_1"><g data-mml-node="msub" data-latex="\varphi_1 "><g data-mml-node="mi" data-latex="\varphi"><path data-c="1D711" d="M503 442C486 442 471 439 456 434 393 413 349 351 324 294 282 201 270 163 239 58 136 79 84 126 84 200 84 267 131 364 164 402 170 409 173 414 173 417 173 426 168 431 157 431 140 431 118 402 91 344 64 286 50 234 50 189 50 85 129 19 220-3L169-165C165-176 163-183 163-186 163-207 174-218 196-218 215-218 228-208 236-189L270-12C281-13 290-13 299-13 381-13 454 19 520 83 586 147 619 220 619 302 619 380 578 442 503 442M583 280C583 217 553 162 492 115 435 73 374 52 308 52 302 52 296 52 291 53 285 53 282 53 282 52 297 131 306 178 310 192 333 271 401 377 493 377 549 377 583 337 583 280Z"></path></g><g data-mml-node="mn" transform="translate(687,-150) scale(0.707)" data-latex="1"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g></g></g></g></svg></mjx-container>,<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.493ex" xmlns="http://www.w3.org/2000/svg" width="2.467ex" height="1.493ex" role="img" focusable="false" viewBox="0 -442 1090.6 660"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\varphi_2"><g data-mml-node="msub" data-latex="\varphi_2 "><g data-mml-node="mi" data-latex="\varphi"><path data-c="1D711" d="M503 442C486 442 471 439 456 434 393 413 349 351 324 294 282 201 270 163 239 58 136 79 84 126 84 200 84 267 131 364 164 402 170 409 173 414 173 417 173 426 168 431 157 431 140 431 118 402 91 344 64 286 50 234 50 189 50 85 129 19 220-3L169-165C165-176 163-183 163-186 163-207 174-218 196-218 215-218 228-208 236-189L270-12C281-13 290-13 299-13 381-13 454 19 520 83 586 147 619 220 619 302 619 380 578 442 503 442M583 280C583 217 553 162 492 115 435 73 374 52 308 52 302 52 296 52 291 53 285 53 282 53 282 52 297 131 306 178 310 192 333 271 401 377 493 377 549 377 583 337 583 280Z"></path></g><g data-mml-node="mn" transform="translate(687,-150) scale(0.707)" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g></g></svg></mjx-container> 表示两点的纬度；</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.029ex" xmlns="http://www.w3.org/2000/svg" width="3.204ex" height="1.649ex" role="img" focusable="false" viewBox="0 -716 1416 729"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\Delta\lambda"><g data-mml-node="mi" data-latex="\Delta"><path data-c="394" d="M759 0C776 0 785 4 785 13L445 696C438 709 429 716 416 716 403 716 394 709 387 696L52 25C49 18 47 14 47 12 47 4 56 0 73 0M384 604 644 83 124 83Z"></path></g><g data-mml-node="mi" data-latex="\lambda" transform="translate(833,0)"><path data-c="1D706" d="M86-13C97-13 109-6 122 9L355 285C390 189 416 117 433 68 444 37 451 19 456 12 467-3 486-11 512-11L533-11C543-10 548-6 548 3 548 5 546 9 542 14 535 21 528 36 520 59L319 621C302 670 261 694 196 694 181 694 174 689 174 679 174 672 180 667 191 664 205 660 214 655 219 649 226 641 236 621 247 589L342 322 72 53C59 40 53 29 53 20 53 2 68-13 86-13Z"></path></g></g></g></svg></mjx-container> 表示两点经度的差值。</p></div><div class="story post-story"><h2 id="距离计算函数"><a href="#距离计算函数" class="headerlink" title="距离计算函数"></a>距离计算函数</h2><p>下面就是计算球面间两点 (lat0, lng)-(lat1, lng1) 之间距离的函数。</p><figure class="highlight python"><table><tbody><tr><td class="code"><pre><span class="line"><span class="keyword">from</span> math <span class="keyword">import</span> sin, asin, cos, radians, fabs, sqrt</span><br><span class="line"> </span><br><span class="line">EARTH_RADIUS=<span class="number">6371</span> <span class="comment"># 地球平均半径，6371km</span></span><br><span class="line"> </span><br><span class="line"><span class="keyword">def</span> <span class="title function_">hav</span>(<span class="params">theta</span>):</span><br><span class="line"> s = sin(theta / <span class="number">2</span>)</span><br><span class="line"> <span class="keyword">return</span> s * s</span><br><span class="line"> </span><br><span class="line"><span class="keyword">def</span> <span class="title function_">get_distance_hav</span>(<span class="params">lat0, lng0, lat1, lng1</span>):</span><br><span class="line"> <span class="string">"用haversine公式计算球面两点间的距离。"</span></span><br><span class="line"> <span class="comment"># 经纬度转换成弧度</span></span><br><span class="line"> lat0 = radians(lat0)</span><br><span class="line"> lat1 = radians(lat1)</span><br><span class="line"> lng0 = radians(lng0)</span><br><span class="line"> lng1 = radians(lng1)</span><br><span class="line"> </span><br><span class="line"> dlng = fabs(lng0 - lng1)</span><br><span class="line"> dlat = fabs(lat0 - lat1)</span><br><span class="line"> h = hav(dlat) + cos(lat0) * cos(lat1) * hav(dlng)</span><br><span class="line"> distance = <span class="number">2</span> * EARTH_RADIUS * asin(sqrt(h))</span><br><span class="line"> </span><br><span class="line"> <span class="keyword">return</span> distance</span><br></pre></td></tr></tbody></table></figure></div><div class="story post-story"><h2 id="相关文献"><a href="#相关文献" class="headerlink" title="相关文献"></a>相关文献</h2><p><a target="_blank" rel="external nofollow noopener noreferrer" href="/go.html?u=aHR0cDovL29yYWNsZS1hYmMud2lraWRvdC5jb20vemgtYmxvZzoyMA">LBS 球面距离公式</a></p></div></div><div class="footer"><div class="copyright license"><div class="license-title">LBS 球面距离公式</div><div class="license-link"><a href="https://blog.mhuig.top/p/5e7ad437/">https://blog.mhuig.top/p/5e7ad437/</a></div><div class="license-meta"><div class="license-meta-item"><div class="license-meta-title">本文作者</div><div class="license-meta-text">MHuiG</div></div><div class="license-meta-item"><div class="license-meta-title">发布于</div><div class="license-meta-text">Feb 23, 2020</div></div><div class="license-meta-item"><div class="license-meta-title">更新于</div><div class="license-meta-text">Nov 20, 2025</div></div><div class="license-meta-item"><div class="license-meta-title">许可协议</div><div class="license-meta-text"><a 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