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Quantum Physics

Quantum Tunneling Calculator

Use this quantum tunneling calculator to calculate estimate tunneling probability through a rectangular potential barrier.

quantum tunnelingbarriertransmission probabilityquantum physicsmodern physicsscientific notation

Calculator

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Calculator Inputs

Choose what you want to calculate, enter realistic values, adjust units where shown, and use the scenario section for repeated-use planning.

Input and Formula Breakdown

Transmission decreases rapidly with barrier width, mass, and barrier height above particle energy.

Particle mass
1 m_e
Barrier height
5 eV
Particle energy
2 eV
Barrier width
1 nm
Transmission probability
0.000002%

Scenario and Comparison

Current

0.000002%

Projected

0

Adjusted

0

Visual Comparison

Current result0
Projected usage0
Comparison scenario0

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This calculator is intended for educational and informational purposes. For laboratory, engineering, or research-critical work, verify results using authoritative references.

Trust note

Planning estimate

Use this result as a practical estimate. Real-world conditions, local rules, measurement tolerance, and changing inputs can affect the final outcome.

Medium risk contextDifficulty: professionalConfidence estimate: 95/100Reviewed 2026-05-18Reviewed by: Science content reviewerCalculator vuces-2.1 / Formula vformula-1.03 sources listed

Formula and Explanation

T approx exp(-2 a sqrt(2m(V-E)) / hbar)

This calculator applies the formula T approx exp(-2 a sqrt(2m(V-E)) / hbar). Enter each value with the matching unit, and AZCalculate updates the result instantly.

Variable descriptions

mass(m_e)
Particle mass: Particle mass measured in m_e, entered as a known value.
barrier(eV)
Barrier height: Barrier height measured in eV, entered as a known value.
energy(eV)
Particle energy: Particle energy measured in eV, entered as a known value.
width(nm)
Barrier width: Barrier width measured in nm, entered as a known value.
probability(%)
Target probability: Target probability measured in %, entered as a known value.

Formula Notes

  • Use consistent units for values that are multiplied, divided, or compared.
  • Results may be rounded for readability, while the calculator keeps greater precision internally.
  • Real-world measurements and assumptions can introduce small differences from the calculated estimate.

Common uses

  • Study barrier penetration
  • Estimate tunneling trends
  • Compare particle mass and barrier width
  • Learn modern physics relationships
  • Check formula steps

Assumptions

What this calculation assumes

  • Calculations use idealized quantum and modern physics formulas.
  • Research-critical work should use authoritative references and full significant-figure control.
  • Inputs are assumed to describe the same scenario and use compatible units.
  • Results may be rounded for readability.

Avoid mistakes

Quick checks before you rely on the result

  • Mixing joules and electronvolts.
  • Using nanometers, picometers, and meters without conversion.
  • Mixing units, periods, currencies, or measurement systems without converting first.
  • Rounding intermediate values too early.

Step-by-Step Explanation

Follow the reasoning, not only the final number.

  1. 1

    Set up the calculation

    Enter the known values in the calculator fields.

    Starting with clearly defined values and units prevents the most common calculation errors.

  2. 2

    Work through step 2

    Keep the units consistent with the labels shown beside each input.

    This step transforms the known values into the form required by the formula.

  3. 3

    Work through step 3

    Apply the formula: T approx exp(-2 a sqrt(2m(V-E)) / hbar).

    This step transforms the known values into the form required by the formula.

  4. 4

    Interpret the result

    Review the primary result and supporting values.

    Compare the result with your real-world goal, such as study barrier penetration.

Worked example

Practical quantum tunneling calculator example

Known values

  • Particle mass: 1 m_e
  • Barrier height: 5 eV
  • Particle energy: 2 eV
  • Barrier width: 1 nm

Calculation

  1. 1. Start with the known values shown for this quantum tunneling calculator scenario.
  2. 2. Substitute those values into T approx exp(-2 kappa a).
  3. 3. Evaluate the expression and keep the requested unit and rounding.

Result and meaning

Transmission probability: 0.000002%

Calculator guide

About this Quantum Tunneling Calculator

Estimate tunneling probability through a rectangular potential barrier. This page includes an interactive calculator, concise formula notes, worked examples, FAQs, related calculators, and practical guidance you can revisit whenever needed.

quantum tunnelingbarriertransmission probabilityquantum physicsmodern physicsscientific notation

References

Sources used for this calculator

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Calculator usage

Usage information loads after the calculator is ready.

FAQ

Quantum Tunneling Calculator FAQs

How does the quantum tunneling calculator work?+

It uses T approx exp(-2 a sqrt(2m(V-E)) / hbar) and calculates the result from the values you enter.

Can I copy or print the result?+

Yes. AZCalculate calculator pages include copy, share, and print actions.

How should I use this calculator result?+

Use it as an estimate and compare it with the formula, assumptions, and examples shown on the page.

Why can real-world results differ?+

Real-world inputs can include local rules, changing rates, measurement tolerances, and conditions outside the core formula.

What information do I need for the quantum tunneling calculator?+

Enter the known values requested by the calculator. Use the unit selectors where available and make sure the values describe the same scenario.

How accurate is the quantum tunneling calculator?+

The calculator follows the formula shown on this page. Accuracy depends on the values, units, assumptions, and rounding used in your scenario.

Can I change the currency or measurement system?+

Yes. Use the country, currency, and unit-system controls. Supported calculators apply those preferences and shared links preserve them.

Can I share or print my calculation?+

Yes. You can share through WhatsApp, Facebook, X, or LinkedIn, copy a link, create a QR code, and print or save a formatted report as PDF.

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Quantum Tunneling Calculator - AZCalculate | AZCalculate