Quantum computation is modeled by quantum circuits. All the quantum operations are reversible so the quantum circuits can be built using reversible logic gates. Reversible computing is the emerging technology; its major role is in the field of quantum computing, optical computing, and design of low power nanocircuits. The most frequently used computational unit for digital signal processing and multimedia applications is multiplier. To compute square of an operand, regular multipliers are used in general. This paper proposes a dedicated quantum circuit for computing square of an operand efficiently compared to the existing multipliers in the literature. The squaring unit is mathematically modeled and its metrics quantum cost, garbage outputs and ancilla input, gate count are calculated. We compared the proposed design with the existing multipliers to compute square and found that proposed square unit is efficient in terms of quantum cost, garbage outputs, ancilla inputs and gate count. The proposed reversible square circuit has 63% to 85% improvement of quantum cost, garbage outputs, ancilla inputs and gate count over existing reversible multiplier circuits.