diff --git a/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/WebMercatorAlgebra.kt b/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/WebMercatorAlgebra.kt
index f4ea339b8..959146072 100644
--- a/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/WebMercatorAlgebra.kt
+++ b/kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/WebMercatorAlgebra.kt
@@ -9,24 +9,55 @@ import space.kscience.kmath.operations.Algebra
 import kotlin.math.*
 
 public class GeodeticCoordinates private constructor(public val latitude: Double, public val longitude: Double) {
-    init {
-        require(longitude in (-PI)..(PI)) { "Longitude $longitude is not in (-PI)..(PI)" }
-        require(latitude in (-PI / 2)..(PI / 2)) { "Latitude $latitude is not in (-PI/2)..(PI/2)" }
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other == null || this::class != other::class) return false
+
+        other as GeodeticCoordinates
+
+        if (latitude != other.latitude) return false
+        if (longitude != other.longitude) return false
+
+        return true
     }
 
-    public companion object {
-        public fun ofRadians(longitude: Double, latitude: Double): GeodeticCoordinates =
-            GeodeticCoordinates(latitude, longitude)
+    override fun hashCode(): Int {
+        var result = latitude.hashCode()
+        result = 31 * result + longitude.hashCode()
+        return result
+    }
 
-        public fun ofDegrees(longitude: Double, latitude: Double): GeodeticCoordinates =
-            GeodeticCoordinates(latitude * PI / 180, longitude * PI / 180)
+    override fun toString(): String {
+        return "GeodeticCoordinates(latitude=$latitude, longitude=$longitude)"
+    }
+
+
+    public companion object {
+        public fun ofRadians(latitude: Double, longitude: Double): GeodeticCoordinates {
+            require(longitude in (-PI)..(PI)) { "Longitude $longitude is not in (-PI)..(PI)" }
+            return GeodeticCoordinates(latitude, longitude.rem(PI / 2))
+        }
+
+        public fun ofDegrees(latitude: Double, longitude: Double): GeodeticCoordinates {
+            require(latitude in (-90.0)..(90.0)) { "Latitude $latitude is not in -90..90" }
+            return GeodeticCoordinates(latitude * PI / 180, (longitude.rem(180) * PI / 180))
+        }
     }
 }
 
 public data class WebMercatorCoordinates(val zoom: Double, val x: Double, val y: Double)
 
 public object WebMercatorAlgebra : Algebra<WebMercatorCoordinates> {
-    fun WebMercatorCoordinates.toGeodetic(): GeodeticCoordinates = TODO()
+
+    private fun scaleFactor(zoom: Double) = 256.0 / 2 / PI * 2.0.pow(zoom)
+
+    public fun WebMercatorCoordinates.toGeodetic(): GeodeticCoordinates {
+        val scaleFactor = scaleFactor(zoom)
+        val longitude = x / scaleFactor - PI
+        val latitude = (atan(exp(PI - y / scaleFactor)) - PI / 4) * 2
+        return GeodeticCoordinates.ofRadians(latitude, longitude)
+    }
 
     /**
      * https://en.wikipedia.org/wiki/Web_Mercator_projection#Formulas
@@ -34,7 +65,7 @@ public object WebMercatorAlgebra : Algebra<WebMercatorCoordinates> {
     public fun GeodeticCoordinates.toMercator(zoom: Double): WebMercatorCoordinates {
         require(abs(latitude) <= 2 * atan(E.pow(PI)) - PI / 2) { "Latitude exceeds the maximum latitude for mercator coordinates" }
 
-        val scaleFactor = 256.0 / 2 / PI * 2.0.pow(zoom)
+        val scaleFactor = scaleFactor(zoom)
         return WebMercatorCoordinates(
             zoom = zoom,
             x = scaleFactor * (longitude + PI),
@@ -56,8 +87,8 @@ public object WebMercatorAlgebra : Algebra<WebMercatorCoordinates> {
             tan(PI / 4 + target.latitude / 2) / tan(PI / 4 + base.latitude / 2)
         )
 
-        val computedZoom = zoom ?: floor( log2(PI / max(abs(xOffsetUnscaled), abs(yOffsetUnscaled))))
-        val scaleFactor = 256.0 / 2 / PI * 2.0.pow(computedZoom)
+        val computedZoom = zoom ?: floor(log2(PI / max(abs(xOffsetUnscaled), abs(yOffsetUnscaled))))
+        val scaleFactor = scaleFactor(computedZoom)
         return WebMercatorCoordinates(
             computedZoom,
             x = scaleFactor * xOffsetUnscaled,
diff --git a/kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/MercatorTest.kt b/kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/MercatorTest.kt
index 5514e5521..81b74ff6e 100644
--- a/kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/MercatorTest.kt
+++ b/kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/MercatorTest.kt
@@ -6,19 +6,35 @@
 package space.kscience.kmath.geometry
 
 import kotlin.test.Test
+import kotlin.test.assertEquals
 import kotlin.test.assertTrue
 
 class MercatorTest {
 
     @Test
-    fun mercatorOffset(){
+    fun boundaries() {
+        assertEquals(GeodeticCoordinates.ofDegrees(45.0, 20.0), GeodeticCoordinates.ofDegrees(45.0, 200.0))
+    }
+
+    @Test
+    fun webMercatorConversion() = with(WebMercatorAlgebra) {
+        val mskCoordinates = GeodeticCoordinates.ofDegrees(55.7558, 37.6173)
+        val m = mskCoordinates.toMercator(2.0)
+        val r = m.toGeodetic()
+
+        assertEquals(mskCoordinates.longitude, r.longitude,1e-4)
+        assertEquals(mskCoordinates.latitude, r.latitude,1e-4)
+    }
+
+    @Test
+    fun webMercatorOffset() {
         val mskCoordinates = GeodeticCoordinates.ofDegrees(55.7558, 37.6173)
         val spbCoordinates = GeodeticCoordinates.ofDegrees(59.9311, 30.3609)
 
-        val offset =  WebMercatorAlgebra.computeOffset(mskCoordinates, spbCoordinates)
+        val offset = WebMercatorAlgebra.computeOffset(mskCoordinates, spbCoordinates)
 
         assertTrue { offset.x in -127.0..128.0 }
         assertTrue { offset.y in -127.0..128.0 }
-        assertTrue { offset.zoom > 1.0 }
+        assertTrue { offset.zoom > 0.0 }
     }
 }
\ No newline at end of file