diff --git a/Cargo.toml b/Cargo.toml
index f09fc66..d6901d2 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -10,6 +10,10 @@ bench = false
 name = "batch"
 harness = false
 
+[[bench]]
+name = "gaussian"
+harness = false
+
 [dependencies]
 approx = { version = "0.5.1", optional = true }
 
diff --git a/benches/gaussian.rs b/benches/gaussian.rs
new file mode 100644
index 0000000..133933b
--- /dev/null
+++ b/benches/gaussian.rs
@@ -0,0 +1,50 @@
+use criterion::{criterion_group, criterion_main, Criterion};
+use trueskill_tt::gaussian::Gaussian;
+
+fn benchmark_gaussian_arithmetic(criterion: &mut Criterion) {
+    // Define test Gaussians
+    let g1 = Gaussian::from_ms(25.0, 25.0 / 3.0);
+    let g2 = Gaussian::from_ms(0.0, 1.0);
+    let g3 = Gaussian::from_ms(1.0, 1.0);
+    
+    // Benchmark addition
+    criterion.bench_function("Gaussian::add", |bencher| {
+        bencher.iter(|| g1 + g2);
+    });
+    
+    // Benchmark subtraction
+    criterion.bench_function("Gaussian::sub", |bencher| {
+        bencher.iter(|| g1 - g3);
+    });
+    
+    // Benchmark multiplication
+    criterion.bench_function("Gaussian::mul", |bencher| {
+        bencher.iter(|| g1 * g2);
+    });
+    
+    // Benchmark division
+    criterion.bench_function("Gaussian::div", |bencher| {
+        bencher.iter(|| g1 / g2);
+    });
+    
+    // Benchmark natural parameter conversions
+    criterion.bench_function("Gaussian::pi", |bencher| {
+        bencher.iter(|| g1.pi());
+    });
+    
+    criterion.bench_function("Gaussian::tau", |bencher| {
+        bencher.iter(|| g1.tau());
+    });
+    
+    // Benchmark combined pi/tau operations (used in mul/div)
+    criterion.bench_function("Gaussian::pi_tau_combined", |bencher| {
+        bencher.iter(|| {
+            let pi = g1.pi();
+            let tau = g1.tau();
+            (pi, tau)
+        });
+    });
+}
+
+criterion_group!(benches, benchmark_gaussian_arithmetic);
+criterion_main!(benches);