The prospects for measuring the branching fraction of $$H \rightarrow \mu ^{+} \mu ^{-}$$
H
→
μ
+
μ
-
at the International Linear Collider (ILC) have been evaluated based on a full detector simulation of the International Large Detector (ILD) concept, considering centre-of-mass energies ($$\sqrt{s}$$
s
) of 250 GeV and 500 GeV with two different beam polarisation configurations of $${\mathcal {P}} (e^{-}, e^{+}) = (-\,80{\%}, +\,30{\%})$$
P
(
e
-
,
e
+
)
=
(
-
80
%
,
+
30
%
)
and $$(+\,80{\%}, -\,30{\%})$$
(
+
80
%
,
-
30
%
)
. For both $$\sqrt{s}$$
s
cases, the two final states $$e^{+} e^{-} \rightarrow q\overline{q}H$$
e
+
e
-
→
q
q
¯
H
and $$e^{+} e^{-} \rightarrow \nu \overline{\nu }H$$
e
+
e
-
→
ν
ν
¯
H
have been analyzed. For integrated luminosities of 2 $$\hbox {ab}^{-1}$$
ab
-
1
at $$\sqrt{s} =250$$
s
=
250
GeV and 4 $$\hbox {ab}^{-1}$$
ab
-
1
at $$\sqrt{s} =500$$
s
=
500
GeV, the combined precision on the branching fraction of $$H \rightarrow \mu ^{+} \mu ^{-}$$
H
→
μ
+
μ
-
is estimated to be 17%. The impact of the transverse momentum resolution for this analysis is also studied.