diff --git a/Tests/test_image_filter.py b/Tests/test_image_filter.py
index 4fa24e2f9c5..e0124dd6f55 100644
--- a/Tests/test_image_filter.py
+++ b/Tests/test_image_filter.py
@@ -235,6 +235,25 @@ def test_invalid_box_blur_filter(radius: int | tuple[int, int]) -> None:
         im.filter(box_blur_filter)
 
 
+@pytest.mark.parametrize("radius", (float("nan"), float("inf"), 2**31))
+def test_out_of_range_blur_filter_radius(radius: float) -> None:
+    im = hopper()
+    with pytest.raises(ValueError, match="radius"):
+        im.filter(ImageFilter.BoxBlur(radius))
+    with pytest.raises(ValueError, match="radius"):
+        im.filter(ImageFilter.GaussianBlur(radius))
+
+
+@pytest.mark.parametrize("radius", (2**24, 2**30))
+def test_large_blur_filter_radius(radius: int) -> None:
+    # A radius this large overflows the accumulators unless they stay unsigned
+    im = Image.new("L", (3, 3), 128)
+    assert im.filter(ImageFilter.BoxBlur(radius)).getpixel((1, 1)) == 128
+
+    im = Image.new("RGB", (3, 3), (128, 128, 128))
+    assert im.filter(ImageFilter.BoxBlur(radius)).getpixel((1, 1)) == (128, 128, 128)
+
+
 def test_rankfilter_size_1() -> None:
     im = Image.new("L", (3, 3), 128)
 
diff --git a/src/libImaging/BoxBlur.c b/src/libImaging/BoxBlur.c
index 4fea4fe44b8..1d70c6ee8c3 100644
--- a/src/libImaging/BoxBlur.c
+++ b/src/libImaging/BoxBlur.c
@@ -40,10 +40,10 @@ void static inline ImagingLineBoxBlur32(
     /* Compute acc for -1 pixel (outside of image):
        From "-radius-1" to "-1" get first pixel,
        then from "0" to "radius-1". */
-    acc[0] = lineIn[0][0] * (radius + 1);
-    acc[1] = lineIn[0][1] * (radius + 1);
-    acc[2] = lineIn[0][2] * (radius + 1);
-    acc[3] = lineIn[0][3] * (radius + 1);
+    acc[0] = lineIn[0][0] * (UINT32)(radius + 1);
+    acc[1] = lineIn[0][1] * (UINT32)(radius + 1);
+    acc[2] = lineIn[0][2] * (UINT32)(radius + 1);
+    acc[3] = lineIn[0][3] * (UINT32)(radius + 1);
     /* As radius can be bigger than xsize, iterate to edgeA -1. */
     for (x = 0; x < edgeA - 1; x++) {
         acc[0] += lineIn[x][0];
@@ -52,10 +52,10 @@ void static inline ImagingLineBoxBlur32(
         acc[3] += lineIn[x][3];
     }
     /* Then multiply remainder to last x. */
-    acc[0] += lineIn[lastx][0] * (radius - edgeA + 1);
-    acc[1] += lineIn[lastx][1] * (radius - edgeA + 1);
-    acc[2] += lineIn[lastx][2] * (radius - edgeA + 1);
-    acc[3] += lineIn[lastx][3] * (radius - edgeA + 1);
+    acc[0] += lineIn[lastx][0] * (UINT32)(radius - edgeA + 1);
+    acc[1] += lineIn[lastx][1] * (UINT32)(radius - edgeA + 1);
+    acc[2] += lineIn[lastx][2] * (UINT32)(radius - edgeA + 1);
+    acc[3] += lineIn[lastx][3] * (UINT32)(radius - edgeA + 1);
 
     if (edgeA <= edgeB) {
         /* Subtract pixel from left ("0").
@@ -123,11 +123,11 @@ void static inline ImagingLineBoxBlur8(
 
 #define SAVE(x, bulk) lineOut[x] = (UINT8)((bulk + (1 << 23)) >> 24)
 
-    acc = lineIn[0] * (radius + 1);
+    acc = lineIn[0] * (UINT32)(radius + 1);
     for (x = 0; x < edgeA - 1; x++) {
         acc += lineIn[x];
     }
-    acc += lineIn[lastx] * (radius - edgeA + 1);
+    acc += lineIn[lastx] * (UINT32)(radius - edgeA + 1);
 
     if (edgeA <= edgeB) {
         for (x = 0; x < edgeA; x++) {
@@ -176,7 +176,7 @@ ImagingHorizontalBoxBlur(Imaging imOut, Imaging imIn, float floatRadius) {
 
     int radius = (int)floatRadius;
     UINT32 ww = (UINT32)(1 << 24) / (floatRadius * 2 + 1);
-    UINT32 fw = ((1 << 24) - (radius * 2 + 1) * ww) / 2;
+    UINT32 fw = ((1 << 24) - ((UINT32)radius * 2 + 1) * ww) / 2;
 
     int edgeA = MIN(radius + 1, imIn->xsize);
     int edgeB = MAX(imIn->xsize - radius - 1, 0);
@@ -244,9 +244,14 @@ ImagingBoxBlur(Imaging imOut, Imaging imIn, float xradius, float yradius, int n)
     if (n < 1) {
         return ImagingError_ValueError("number of passes must be greater than zero");
     }
-    if (xradius < 0 || yradius < 0) {
+    /* Negated comparisons, so that NaN is rejected as well. */
+    if (!(xradius >= 0) || !(yradius >= 0)) {
         return ImagingError_ValueError("radius must be >= 0");
     }
+    /* 2**31 and above cannot be converted to an int. */
+    if (xradius >= 2147483648.0f || yradius >= 2147483648.0f) {
+        return ImagingError_ValueError("radius too large");
+    }
 
     if (imIn->mode != imOut->mode || imIn->type != imOut->type ||
         imIn->bands != imOut->bands || imIn->xsize != imOut->xsize ||