diff --git a/gsplat/cuda/_torch_impl.py b/gsplat/cuda/_torch_impl.py
index 892c6a66..5de19f1f 100644
--- a/gsplat/cuda/_torch_impl.py
+++ b/gsplat/cuda/_torch_impl.py
@@ -306,20 +306,27 @@ def _fully_fused_projection(
 
     depths = means_c[..., 2]  # [C, N]
 
+    # scale factor for 3 sigma in 2 dimension for a 2d multivariate gaussian
+    # distribution
+    scale_factor = 3.4086
+    # calculating magnitude of major and and minor axis
     b = (covars2d[..., 0, 0] + covars2d[..., 1, 1]) / 2  # (...,)
     v1 = b + torch.sqrt(torch.clamp(b**2 - det, min=0.01))  # (...,)
-    radius = torch.ceil(3.0 * torch.sqrt(v1))  # (...,)
+    radius = torch.ceil(scale_factor * torch.sqrt(v1))  # (...,)
     # v2 = b - torch.sqrt(torch.clamp(b**2 - det, min=0.01))  # (...,)
-    # radius = torch.ceil(3.0 * torch.sqrt(torch.max(v1, v2)))  # (...,)
+    # radius = torch.ceil(scale_factor * torch.sqrt(torch.max(v1, v2)))  # (...,)
+
+    x_proj = scale_factor * torch.sqrt(covars2d[..., 0, 0])  # (...,)
+    y_proj = scale_factor * torch.sqrt(covars2d[..., 1, 1])  # (...,)
 
     valid = (det > 0) & (depths > near_plane) & (depths < far_plane)
     radius[~valid] = 0.0
 
     inside = (
-        (means2d[..., 0] + radius > 0)
-        & (means2d[..., 0] - radius < width)
-        & (means2d[..., 1] + radius > 0)
-        & (means2d[..., 1] - radius < height)
+        (means2d[..., 0] + x_proj > 0)
+        & (means2d[..., 0] - x_proj < width)
+        & (means2d[..., 1] + y_proj > 0)
+        & (means2d[..., 1] - y_proj < height)
     )
     radius[~inside] = 0.0
 
diff --git a/gsplat/cuda/csrc/fully_fused_projection_fwd.cu b/gsplat/cuda/csrc/fully_fused_projection_fwd.cu
index c651e803..8e70cefc 100644
--- a/gsplat/cuda/csrc/fully_fused_projection_fwd.cu
+++ b/gsplat/cuda/csrc/fully_fused_projection_fwd.cu
@@ -162,11 +162,14 @@ __global__ void fully_fused_projection_fwd_kernel(
     inverse(covar2d, covar2d_inv);
 
     // take 3 sigma as the radius (non differentiable)
+    T scale_factor = 3.4086;
     T b = 0.5f * (covar2d[0][0] + covar2d[1][1]);
     T v1 = b + sqrt(max(0.01f, b * b - det));
-    T radius = ceil(3.f * sqrt(v1));
+    T radius = ceil(scale_factor * sqrt(v1));
     // T v2 = b - sqrt(max(0.1f, b * b - det));
     // T radius = ceil(3.f * sqrt(max(v1, v2)));
+    T x_proj = scale_factor * sqrt(covar2d[0][0]);
+    T y_proj = scale_factor * sqrt(covar2d[1][1]);
 
     if (radius <= radius_clip) {
         radii[idx] = 0;
@@ -174,8 +177,8 @@ __global__ void fully_fused_projection_fwd_kernel(
     }
 
     // mask out gaussians outside the image region
-    if (mean2d.x + radius <= 0 || mean2d.x - radius >= image_width ||
-        mean2d.y + radius <= 0 || mean2d.y - radius >= image_height) {
+    if (mean2d.x + x_proj <= 0 || mean2d.x - x_proj >= image_width ||
+        mean2d.y + y_proj <= 0 || mean2d.y - y_proj >= image_height) {
         radii[idx] = 0;
         return;
     }
diff --git a/gsplat/cuda/csrc/fully_fused_projection_packed_fwd.cu b/gsplat/cuda/csrc/fully_fused_projection_packed_fwd.cu
index 4d8609f0..213df79b 100644
--- a/gsplat/cuda/csrc/fully_fused_projection_packed_fwd.cu
+++ b/gsplat/cuda/csrc/fully_fused_projection_packed_fwd.cu
@@ -178,18 +178,21 @@ __global__ void fully_fused_projection_packed_fwd_kernel(
     T radius;
     if (valid) {
         // take 3 sigma as the radius (non differentiable)
+        T scale_factor = 3.4086;
         T b = 0.5f * (covar2d[0][0] + covar2d[1][1]);
         T v1 = b + sqrt(max(0.1f, b * b - det));
         T v2 = b - sqrt(max(0.1f, b * b - det));
-        radius = ceil(3.f * sqrt(max(v1, v2)));
+        radius = ceil(scale_factor * sqrt(max(v1, v2)));
+        T x_proj = scale_factor * sqrt(covar2d[0][0]);
+        T y_proj = scale_factor * sqrt(covar2d[1][1]);
 
         if (radius <= radius_clip) {
             valid = false;
         }
 
         // mask out gaussians outside the image region
-        if (mean2d.x + radius <= 0 || mean2d.x - radius >= image_width ||
-            mean2d.y + radius <= 0 || mean2d.y - radius >= image_height) {
+        if (mean2d.x + x_proj <= 0 || mean2d.x - x_proj >= image_width ||
+            mean2d.y + y_proj <= 0 || mean2d.y - y_proj >= image_height) {
             valid = false;
         }
     }