Quantum Tunneling Calculator

Calculate quantum tunneling probability, transmission coefficient, and penetration depth through a potential barrier.

Particle Energy

Barrier Height

Barrier Width

Particle Mass

Tab to move between fields

Tunneling Probability

35.9%

Transmission Coefficient

0.36

Reflection Coefficient

0.641

Decay Constant (κ)5,123,000,000 m⁻¹

Penetration Depth0 m

Barrier Opacity (κL)0.512

How to Use This Calculator

Enter Particle Energy (eV) — the kinetic energy of the particle approaching the barrier.
Enter Barrier Height (eV) — the barrier must be higher than particle energy for quantum tunneling to apply.
Set Barrier Width (m): atomic-scale widths (1e-10 m = 1 Å) produce significant tunneling; wider barriers exponentially suppress it.
Set Particle Mass (kg): the default 9.109e-31 kg is an electron; protons (1.67e-27 kg) tunnel far less.
Read Tunneling Probability (%) and Transmission Coefficient — even small probabilities matter in STM, nuclear fusion, and semiconductor devices.

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Formula

T ≈ e^(-2κL), κ = √(2m(V-E))/ℏ

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