diff --git a/r1cs-std/src/fields/fp/mod.rs b/r1cs-std/src/fields/fp/mod.rs
index 6648864..47d592b 100644
--- a/r1cs-std/src/fields/fp/mod.rs
+++ b/r1cs-std/src/fields/fp/mod.rs
@@ -22,6 +22,22 @@ impl<F: PrimeField> FpGadget<F> {
     pub fn from<CS: ConstraintSystem<F>>(mut cs: CS, value: &F) -> Self {
         Self::alloc(cs.ns(|| "from"), || Ok(*value)).unwrap()
     }
+
+    fn is_constant(&self) -> bool {
+        match &self.variable {
+            // If you don't do alloc_constant, you are guaranteed to get a variable,
+            // hence we assume that all variables are not the constant variable.
+            // Technically this omits recognizing some constants.
+            // E.g. given variables w,x,y,z with constraints:
+            // w = x + 1
+            // y = -x + 1
+            // and then created the variable z = w + y,
+            // this would not recognize that z is in fact a constant.
+            // Since this is an edge case, this is left as a TODO.
+            Var(_v) => false,
+            LC(l) => l.is_constant(),
+        }
+    }
 }
 
 impl<F: PrimeField> FieldGadget<F, F> for FpGadget<F> {
@@ -145,6 +161,14 @@ impl<F: PrimeField> FieldGadget<F, F> for FpGadget<F> {
         mut cs: CS,
         other: &Self,
     ) -> Result<Self, SynthesisError> {
+        // Apply constant folding if it applies
+        // unwrap is used, because these values are guaranteed to exist.
+        if other.is_constant() {
+            return self.mul_by_constant(cs, &other.get_value().unwrap());
+        } else if self.is_constant() {
+            return other.mul_by_constant(cs, &self.get_value().unwrap());
+        }
+
         let product = Self::alloc(cs.ns(|| "mul"), || {
             Ok(self.value.get()? * &other.value.get()?)
         })?;
diff --git a/r1cs-std/src/fields/mod.rs b/r1cs-std/src/fields/mod.rs
index 51e254f..9807958 100644
--- a/r1cs-std/src/fields/mod.rs
+++ b/r1cs-std/src/fields/mod.rs
@@ -290,6 +290,7 @@ pub(crate) mod tests {
         let b_native = FE::rand(&mut rng);
         let a = F::alloc(&mut cs.ns(|| "generate_a"), || Ok(a_native)).unwrap();
         let b = F::alloc(&mut cs.ns(|| "generate_b"), || Ok(b_native)).unwrap();
+        let b_const = F::alloc_constant(&mut cs.ns(|| "generate_b_as_constant"), b_native).unwrap();
 
         let zero = F::zero(cs.ns(|| "zero")).unwrap();
         let zero_native = zero.get_value().unwrap();
@@ -398,6 +399,12 @@ pub(crate) mod tests {
         assert_eq!(ab, ba);
         assert_eq!(ab.get_value().unwrap(), a_native * &b_native);
 
+        let ab_const = a.mul(cs.ns(|| "a_times_b_const"), &b_const).unwrap();
+        let b_const_a = b_const.mul(cs.ns(|| "b_const_times_a"), &a).unwrap();
+        assert_eq!(ab_const, b_const_a);
+        assert_eq!(ab_const, ab);
+        assert_eq!(ab_const.get_value().unwrap(), a_native * &b_native);
+
         // (a * b) * a = a * (b * a)
         let ab_a = ab.mul(cs.ns(|| "ab_times_a"), &a).unwrap();
         let a_ba = a.mul(cs.ns(|| "a_times_ba"), &ba).unwrap();