diff --git a/rms_norm.py b/rms_norm.py
new file mode 100644
index 0000000..f4ba67b
--- /dev/null
+++ b/rms_norm.py
@@ -0,0 +1,119 @@
+import ninetoothed
+import ninetoothed.language as ntl
+import torch
+import torch.nn.functional as F
+import triton
+import triton.language as tl
+from ninetoothed import Symbol, Tensor
+
+BLOCK_SIZE = Symbol("BLOCK_SIZE", constexpr=True)
+
+
+@ninetoothed.jit
+def rms_norm_kernel(
+    input: Tensor(2).tile((1, BLOCK_SIZE)),
+    output: Tensor(2).tile((1, BLOCK_SIZE)),
+    eps: Tensor(0),
+):
+    input_fp32 = ntl.cast(input, ntl.float32)
+    output = input_fp32 * ntl.rsqrt(  # noqa: F841
+        ntl.sum(input_fp32 * input_fp32) / input.shape[-1] + eps
+    )
+
+
+def rms_norm(input, eps=1e-5):
+    output = torch.empty_like(input)
+
+    rms_norm_kernel(input, output, eps, BLOCK_SIZE=input.shape[-1])
+
+    return output
+
+
+@triton.jit
+def triton_rms_norm_kernel(
+    input_ptr,
+    output_ptr,
+    num_cols,
+    input_row_stride,
+    output_row_stride,
+    eps: tl.constexpr,
+    BLOCK_SIZE: tl.constexpr,
+):
+    row_idx = tl.program_id(0)
+
+    col_offsets = tl.arange(0, BLOCK_SIZE)
+    input_ptrs = input_ptr + row_idx * input_row_stride + col_offsets
+    mask = col_offsets < num_cols
+    input = tl.load(input_ptrs, mask=mask)
+
+    output = input * tl.rsqrt(tl.sum(input * input) / num_cols + eps)
+
+    output_ptrs = output_ptr + row_idx * output_row_stride + col_offsets
+    tl.store(output_ptrs, output, mask=mask)
+
+
+def triton_rms_norm(input, eps=1e-5):
+    output = torch.empty_like(input)
+
+    triton_rms_norm_kernel[(input.shape[-2],)](
+        input,
+        output,
+        input.shape[-1],
+        input.stride(-2),
+        output.stride(-2),
+        eps,
+        BLOCK_SIZE=triton.next_power_of_2(input.shape[-1]),
+    )
+
+    return output
+
+
+if __name__ == "__main__":
+    torch.manual_seed(0)
+    input = torch.randn(1151, 8192, dtype=torch.float16, device="cuda")
+    ninetoothed_output = rms_norm(input)
+    torch_output = F.rms_norm(input, input.shape[-1:])
+    triton_output = triton_rms_norm(input)
+    print(ninetoothed_output)
+    print(torch_output)
+    print(triton_output)
+    if torch.allclose(ninetoothed_output, torch_output):
+        print("✅ NineToothed and PyTorch match.")
+    else:
+        print("❌ NineToothed and PyTorch differ.")
+    if torch.allclose(ninetoothed_output, triton_output):
+        print("✅ NineToothed and Triton match.")
+    else:
+        print("❌ NineToothed and Triton differ.")
+
+    @triton.testing.perf_report(
+        triton.testing.Benchmark(
+            x_names=["n"],
+            x_vals=[512 * i for i in range(2, 32)],
+            line_arg="provider",
+            line_vals=["ninetoothed", "torch", "triton"],
+            line_names=["NineToothed", "PyTorch", "Triton"],
+            styles=[("blue", "-"), ("green", "-"), ("orange", "-")],
+            ylabel="GB/s",
+            plot_name="rms-norm-performance",
+            args={"m": 4096},
+        )
+    )
+    def benchmark(m, n, provider):
+        input = torch.randn(m, n, dtype=torch.float16, device="cuda")
+
+        if provider == "ninetoothed":
+            ms = triton.testing.do_bench(lambda: rms_norm(input))
+        elif provider == "torch":
+            ms = triton.testing.do_bench(
+                lambda: torch.rms_norm(input, input.shape[-1:])
+            )
+        elif provider == "triton":
+            ms = triton.testing.do_bench(lambda: triton_rms_norm(input))
+
+        def gbps(ms):
+            return 2 * input.numel() * input.element_size() * 1e-6 / ms
+
+        return gbps(ms)
+
+    benchmark.run(show_plots=True, print_data=True, save_path=".")