diff --git a/src/libstd/sys/windows/time.rs b/src/libstd/sys/windows/time.rs
index 20ceff0aa69..209460df10b 100644
--- a/src/libstd/sys/windows/time.rs
+++ b/src/libstd/sys/windows/time.rs
@@ -12,6 +12,8 @@
 use time::Duration;
 use sync::{Once, ONCE_INIT};
 
+const NANOS_PER_SEC: i64 = 1_000_000_000;
+
 pub struct SteadyTime {
     t: libc::LARGE_INTEGER,
 }
@@ -24,7 +26,7 @@ pub fn now() -> SteadyTime {
     }
 
     pub fn ns(&self) -> u64 {
-        self.t as u64 * 1_000_000_000 / frequency() as u64
+        mul_div_i64(self.t as i64, NANOS_PER_SEC, frequency() as i64) as u64
     }
 }
 
@@ -45,6 +47,27 @@ impl<'a> Sub for &'a SteadyTime {
 
     fn sub(self, other: &SteadyTime) -> Duration {
         let diff = self.t as i64 - other.t as i64;
-        Duration::microseconds(diff * 1_000_000 / frequency() as i64)
+        Duration::nanoseconds(mul_div_i64(diff, NANOS_PER_SEC, frequency() as i64))
     }
 }
+
+// Computes (value*numer)/denom without overflow, as long as both
+// (numer*denom) and the overall result fit into i64 (which is the case
+// for our time conversions).
+fn mul_div_i64(value: i64, numer: i64, denom: i64) -> i64 {
+    let q = value / denom;
+    let r = value % denom;
+    // Decompose value as (value/denom*denom + value%denom),
+    // substitute into (value*numer)/denom and simplify.
+    // r < denom, so (denom*numer) is the upper bound of (r*numer)
+    q * numer + r * numer / denom
+}
+
+#[test]
+fn test_muldiv() {
+    assert_eq!(mul_div_i64( 1_000_000_000_001, 1_000_000_000, 1_000_000),  1_000_000_000_001_000);
+    assert_eq!(mul_div_i64(-1_000_000_000_001, 1_000_000_000, 1_000_000), -1_000_000_000_001_000);
+    assert_eq!(mul_div_i64(-1_000_000_000_001,-1_000_000_000, 1_000_000),  1_000_000_000_001_000);
+    assert_eq!(mul_div_i64( 1_000_000_000_001, 1_000_000_000,-1_000_000), -1_000_000_000_001_000);
+    assert_eq!(mul_div_i64( 1_000_000_000_001,-1_000_000_000,-1_000_000),  1_000_000_000_001_000);
+}