diff --git a/src/index.js b/src/index.js
index 86ab489..510103c 100644
--- a/src/index.js
+++ b/src/index.js
@@ -29,6 +29,10 @@ export {
   sqrt as scaleSqrt
 } from "./pow.js";
 
+export {
+  default as scaleRadial
+} from "./radial.js";
+
 export {
   default as scaleQuantile
 } from "./quantile.js";
diff --git a/src/radial.js b/src/radial.js
new file mode 100644
index 0000000..5c76707
--- /dev/null
+++ b/src/radial.js
@@ -0,0 +1,51 @@
+import linear, {linearish} from "./linear.js";
+import number from "./number.js";
+
+function square(x) {
+  return (x < 0 ? -1 : 1) * x * x;
+}
+
+function unsquare(x) {
+  return (x < 0 ? -1 : 1) * Math.sqrt(Math.abs(x));
+}
+
+export default function radial() {
+  var squared = linear(),
+      range = [0, 1],
+      round = false;
+
+  function scale(x) {
+    var y = unsquare(squared(x));
+    return round ? Math.round(y) : y;
+  }
+
+  scale.invert = function(y) {
+    return squared.invert(square(y));
+  };
+
+  scale.domain = function(_) {
+    return arguments.length ? (squared.domain(_), scale) : squared.domain();
+  };
+
+  scale.range = function(_) {
+    return arguments.length ? (squared.range((range = Array.from(_, number)).map(square)), scale) : range.slice();
+  };
+
+  scale.round = function(_) {
+    return arguments.length ? (round = !!_, scale) : round;
+  };
+
+  scale.clamp = function(_) {
+    return arguments.length ? (squared.clamp(_), scale) : squared.clamp();
+  };
+
+  scale.copy = function() {
+    return radial()
+        .domain(squared.domain())
+        .range(range)
+        .round(round)
+        .clamp(squared.clamp());
+  };
+
+  return linearish(scale);
+}
diff --git a/test/radial-test.js b/test/radial-test.js
new file mode 100644
index 0000000..e34c6ec
--- /dev/null
+++ b/test/radial-test.js
@@ -0,0 +1,50 @@
+var tape = require("tape"),
+    scale = require("../");
+
+tape("scaleRadial() has the expected defaults", function(test) {
+  var s = scale.scaleRadial();
+  test.deepEqual(s.domain(), [0, 1]);
+  test.deepEqual(s.range(), [0, 1]);
+  test.equal(s.clamp(), false);
+  test.equal(s.round(), false);
+  test.end();
+});
+
+tape("radial(x) maps a domain value x to a range value y", function(test) {
+  test.equal(scale.scaleRadial().range([1, 2])(0.5), 1.5811388300841898);
+  test.end();
+});
+
+tape("radial(x) ignores extra range values if the domain is smaller than the range", function(test) {
+  test.equal(scale.scaleRadial().domain([-10, 0]).range([2, 3, 4]).clamp(true)(-5), 2.5495097567963922);
+  test.equal(scale.scaleRadial().domain([-10, 0]).range([2, 3, 4]).clamp(true)(50), 3);
+  test.end();
+});
+
+tape("radial(x) ignores extra domain values if the range is smaller than the domain", function(test) {
+  test.equal(scale.scaleRadial().domain([-10, 0, 100]).range([2, 3]).clamp(true)(-5), 2.5495097567963922);
+  test.equal(scale.scaleRadial().domain([-10, 0, 100]).range([2, 3]).clamp(true)(50), 3);
+  test.end();
+});
+
+tape("radial(x) maps an empty domain to the middle of the range", function(test) {
+  test.equal(scale.scaleRadial().domain([0, 0]).range([1, 2])(0), 1.5811388300841898);
+  test.equal(scale.scaleRadial().domain([0, 0]).range([2, 1])(1), 1.5811388300841898);
+  test.end();
+});
+
+tape("radial(x) can map a bilinear domain with two values to the corresponding range", function(test) {
+  var s = scale.scaleRadial().domain([1, 2]);
+  test.deepEqual(s.domain(), [1, 2]);
+  test.equal(s(0.5), -0.7071067811865476);
+  test.equal(s(1.0),  0.0);
+  test.equal(s(1.5),  0.7071067811865476);
+  test.equal(s(2.0),  1.0);
+  test.equal(s(2.5),  1.224744871391589);
+  test.equal(s.invert(-0.5), 0.75);
+  test.equal(s.invert( 0.0), 1.0);
+  test.equal(s.invert( 0.5), 1.25);
+  test.equal(s.invert( 1.0), 2.0);
+  test.equal(s.invert( 1.5), 3.25);
+  test.end();
+});