Nuclear Fuel Burnup Calculator

Compute fuel burnup from reactor operating parameters or estimate U-235 depletion from burnup and initial enrichment.

Reactor Thermal Power

MW_th

Total Fuel Loading

Operating Days

days

Capacity Factor

Discharge Burnup

MWd/tU

Initial U-235 Enrichment

wt%

Total Fuel Mass

Pu-239 Contribution to Fission Power

Fuel Burnup

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Specific Power

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Total Energy

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Total Energy (TJ)

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Est. U-235 Fissioned

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U-235 Remaining

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U-235 Initial

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U-235 Fissioned

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Depletion Fraction

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Final Enrichment

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Est. Pu-239 Produced

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🔆 What is Nuclear Fuel Burnup?

Nuclear fuel burnup is the measure of how much energy has been extracted from nuclear fuel, expressed in megawatt-days per metric ton of uranium (MWd/tU). A burnup of 33,000 MWd/tU means the fuel produced 33,000 megawatt-days of thermal energy for every metric ton of uranium in the reactor core. Burnup is the single most important parameter in nuclear fuel management because it determines fuel lifetime, spent fuel radioactivity, and overall fuel cycle costs.

In a nuclear power plant, fresh fuel containing 3 to 5% U-235 is loaded into the reactor and steadily depleted as fission reactions convert fissile material into energy and fission products. As burnup accumulates, the U-235 content drops and plutonium-239 (bred from U-238 capture) begins to contribute an increasing fraction of the fission power. At typical LWR discharge burnup of 33,000 to 45,000 MWd/tU, Pu-239 accounts for 25 to 35% of total fission energy. Burnup directly relates to the residence time and power history of the fuel in the core.

The burnup formula is BU = P_th × t_op × CF / M_fuel, where P_th is the reactor thermal power in megawatts, t_op is the operating time in days, CF is the capacity factor (fraction of time at full power), and M_fuel is the initial uranium loading in metric tons. The inverse calculation, fuel depletion, uses the burnup value to estimate the residual U-235 content, the fraction of initial fissile material consumed, and the net plutonium retained in the spent fuel.

The specific power (kW/kgU) connects burnup rate to fuel lifetime. A PWR at 35 kW/kgU reaches 33,000 MWd/tU after roughly 943 effective full-power days (EFPD), corresponding to 3 fuel cycles. Higher burnup reduces the volume of spent nuclear fuel generated per unit of electricity and improves fuel economics, making it a key target in reactor design improvements. This calculator covers both the forward calculation (power to burnup) and the reverse (burnup to U-235 depletion), with a simple Pu-239 production estimate for LWR conditions.

📐 Formula

BU = (P_th × t_op × CF) ÷ M_fuel

BU = burnup (MWd/tU)

P_th = reactor thermal power (MW)

t_op = operating days

CF = capacity factor (fraction, e.g. 0.85 for 85%)

M_fuel = initial uranium fuel mass (tU)

Example: 3000 MW, 90 tU, 365 days, 85% CF: BU = 3000 × 365 × 0.85 / 90 = 10,342 MWd/tU

For the fuel depletion calculation, the key conversion is that 1 MWd of thermal energy from U-235 fission consumes approximately 1.023 g of U-235 (from 200 MeV per fission and Avogadro's number). In a real LWR, Pu-239 also contributes a fraction f of fission power, so effective U-235 consumption per MWd is reduced to 1.023 × (1 − f) g/MWd:

m_U235,dep = BU × 1.023 × (1 − f_Pu) × M_fuel / 1000

m_U235,dep = U-235 fissioned (kg)

f_Pu = Pu-239 fraction of fission power (e.g. 0.27 for 27%)

1.023 g/MWd = theoretical U-235 consumption per MWd (200 MeV/fission, per IAEA)

📖 How to Use This Calculator

Steps for Burnup Calculation Mode

Enter reactor thermal power and fuel loading: Type the thermal power in megawatts and the total uranium mass in metric tons (tU). A typical 1000 MWe PWR has about 3000 MW thermal and 80 to 100 tU of fuel in the core.

Set operating duration and capacity factor: Enter operating days and capacity factor in percent. For 3 annual cycles of 365 days each with 85% availability, enter 1095 days and 85%.

Read the burnup result: Click Calculate. The primary result shows discharge burnup in MWd/tU. Specific power, total energy output, and estimated U-235 fissioned are also displayed.

Switch to Depletion mode for spent fuel analysis: Click the Fuel Depletion tab. Enter the discharge burnup, initial enrichment, fuel mass, and Pu fraction. Results include remaining U-235, depletion fraction, final enrichment, and estimated Pu-239.

Adjust Pu contribution for accuracy: Use 20 to 27% Pu fraction for low burnup fuel (under 20,000 MWd/tU) and 30 to 40% for high burnup (above 40,000 MWd/tU). The default of 27% suits a typical 3-cycle PWR batch.

💡 Example Calculations

Example 1: Standard 3-Cycle PWR Campaign

3000 MW reactor, 90 tU fuel, 1095 days (3 years), 85% capacity factor

Effective full-power days (EFPD) = 1095 × 0.85 = 930.75 EFPD.

Burnup = 3000 MW × 930.75 days / 90 tU = 31,025 MWd/tU.

Total energy = 31,025 × 90 = 2,792,250 MWd = 2,792,250 × 24 / 1000 = 67,014 GWh.

Specific power = 3000 / 90 = 33.3 kW/kgU. Estimated U-235 fissioned = 31,025 × 1.023 × 0.70 × 90 / 1000 = 1,989 kg.

Result: 31,025 MWd/tU discharge burnup, 67,014 GWh total energy

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Example 2: Extended Burnup Campaign (High Enrichment)

3300 MW reactor, 80 tU fuel, 1460 days (4 years), 88% capacity factor

EFPD = 1460 × 0.88 = 1284.8 days.

Burnup = 3300 × 1284.8 / 80 = 52,974 MWd/tU (requires 4 to 5% initial enrichment).

Specific power = 3300 / 80 = 41.25 kW/kgU (higher than Example 1, meaning faster burnup accumulation).

Total energy = 52,974 × 80 = 4,237,920 MWd = 101,710 GWh.

Result: 52,974 MWd/tU extended burnup, 41.25 kW/kgU specific power

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Example 3: Spent Fuel Depletion Analysis

Burnup 33,000 MWd/tU, initial enrichment 3.5%, 90 tU core, 27% Pu fraction

Initial U-235 mass = 3.5% × 90 tU × 1000 kg/tU = 3,150 kg.

U-235 fissioned = 33,000 × 1.023 × (1 − 0.27) × 90 / 1000 = 2,220 kg.

U-235 remaining = 3,150 − 2,220 = 930 kg. Depletion = 2220/3150 = 70.5%.

Final enrichment = 930 / 90,000 × 100 = 1.03%. Estimated Pu-239 = 0.17 × 33 × 90 = 505 kg.

Result: 930 kg U-235 remaining at 1.03% final enrichment, 70.5% depletion

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❓ Frequently Asked Questions

What does MWd/tU mean in nuclear fuel burnup?+

MWd/tU stands for megawatt-days per metric ton of uranium. It measures the cumulative thermal energy released per unit mass of fuel. One MWd/tU means one megawatt of thermal power was produced for one day from one metric ton of uranium. A typical PWR fuel assembly is discharged at around 33,000 to 55,000 MWd/tU after several years of irradiation.

How is nuclear fuel burnup calculated from reactor power?+

Burnup (MWd/tU) = P_thermal (MW) x operating days x capacity factor / fuel mass (tU). For a 3000 MW reactor with 90 tU of fuel operating at 85% capacity for 365 days, BU = 3000 x 365 x 0.85 / 90 = 10,342 MWd/tU per year. After three annual cycles, cumulative burnup reaches about 31,000 MWd/tU.

What is the relationship between burnup and U-235 enrichment?+

Higher burnup requires higher initial enrichment because more fissile material is needed to maintain criticality over a longer irradiation period. Standard PWR fuel with 3.5% enrichment achieves about 33,000 MWd/tU. Extended burnup to 55,000 MWd/tU requires 4.5 to 5% enrichment. The NRC limit for light-water reactor fuel is 5% U-235 for standard operation.

How much U-235 remains in spent nuclear fuel?+

Spent PWR fuel discharged at 33,000 MWd/tU starting from 3.5% U-235 enrichment typically retains about 0.9 to 1.1% U-235 by weight, corresponding to about 10 kg/tU out of an initial 35 kg/tU. This represents roughly 70 to 72% depletion of the original U-235 inventory. The remaining U-235 in spent fuel is still enriched above natural uranium (0.72%), which is why it can potentially be reprocessed.

What is effective full-power days (EFPD) in reactor operation?+

Effective full-power days (EFPD) is the equivalent number of days the reactor operates at 100% rated power. If a reactor operates for 365 calendar days at an 85% capacity factor, the EFPD is 365 x 0.85 = 310.25 days. Burnup is proportional to EFPD, not calendar days. EFPD is used to track fuel depletion accurately regardless of actual power variations.

What is specific power and why does it matter?+

Specific power (kW/kgU) is the thermal power per unit mass of uranium in the core. It equals reactor thermal power (kW) divided by fuel loading (kgU), or equivalently MW/tU. Typical PWRs operate at 33 to 40 kW/kgU. Higher specific power means faster burnup accumulation but also higher fission product inventory and heat generation in the fuel, placing greater demands on cladding and coolant.

How is Pu-239 produced and how much is in spent fuel?+

Pu-239 is produced when U-238 absorbs a neutron to form U-239, which decays via Np-239 to Pu-239 with a 2.35-day half-life chain. In a typical PWR at 33,000 MWd/tU discharge, spent fuel contains approximately 5 to 8 kg of total plutonium per metric ton of uranium, of which Pu-239 is 3 to 5 kg/tU. Pu-239 contributes 25 to 35% of fission power at this burnup.

What is the difference between thermal burnup and electrical burnup?+

Burnup is always quoted as thermal energy per unit fuel mass (MWd_th/tU). The thermal-to-electrical conversion introduces a separate efficiency factor of about 32 to 35% for conventional steam-cycle PWRs. A burnup of 33,000 MWd_th/tU translates to about 10,560 to 11,550 MWd_el/tU of net electrical output. Always verify whether a quoted burnup figure refers to thermal or electrical power, as the difference is a factor of about 3.

Why is higher burnup economically beneficial?+

Higher burnup reduces fresh fuel reload quantity per cycle, extends the interval between refueling outages, and decreases the volume of spent fuel generated per unit of electricity. Going from 33,000 to 55,000 MWd/tU reduces spent fuel volume by roughly 40% for the same electrical output. The trade-off is higher initial enrichment cost and more radiation-resistant cladding material such as advanced Zr alloys or silicon carbide composites.

What burnup level makes spent fuel safe for direct disposal?+

All spent nuclear fuel, regardless of burnup, must be stored for decades before final disposal due to heat and radiation from fission products. Higher burnup actually increases the short-term heat output of spent fuel per assembly, requiring longer cooling periods before repository placement. Deep geological repositories are designed to accept fuel at any burnup, but regulatory and repository heat limits may require 40 to 100 years of interim storage in cooling pools or dry casks first.

How does capacity factor affect calculated burnup?+

Capacity factor directly multiplies the calendar operating days in the burnup formula. A reactor running for 365 days at 100% capacity reaches 1.18 times the burnup of the same reactor at 85% capacity over the same period. Typical nuclear plant capacity factors range from 80 to 95%. The world fleet average has exceeded 85% in recent years due to improvements in maintenance scheduling and reduced unplanned outages.

What unit conversions apply to nuclear burnup?+

Common burnup unit conversions: 1 GWd/tU = 1000 MWd/tU; 1 MWd = 24 MWh = 86.4 GJ = 86,400 MJ. The "1 gram U-235 per MWd" approximation comes from 1 MWd requiring approximately 1.023 g of U-235 to fission (based on 200 MeV per fission and Avogadro's number). Specific power conversion: 1 kW/kgU = 1 MW/tU.

🔗 Related Calculators

What is nuclear fuel burnup in MWd/tU?

Nuclear fuel burnup (BU) measures how much energy has been extracted from nuclear fuel, expressed in megawatt-days per metric ton of uranium (MWd/tU). A burnup of 33,000 MWd/tU means the fuel produced 33,000 MW-days of thermal energy per ton of initial uranium loaded.

What is the formula for calculating fuel burnup?

BU (MWd/tU) = P_thermal (MW) x operating days x capacity factor / fuel mass (tU). For example, a 3000 MW reactor with 90 tU fuel operating 365 days at 85% gives BU = 3000 x 365 x 0.85 / 90 = 10,342 MWd/tU per year.

What is a typical burnup for PWR fuel?

Modern PWR fuel is typically discharged at 33,000 to 55,000 MWd/tU after 3 to 4 reactor cycles of 12 to 18 months each. Extended burnup designs can reach 60,000 MWd/tU or higher, requiring initial enrichment of 4 to 5% U-235.

How much U-235 is depleted at typical burnup?

For 3.5% enriched PWR fuel discharged at 33,000 MWd/tU, approximately 70 to 75% of the initial U-235 is consumed. Starting with 35 kg/tU of U-235, the spent fuel contains about 9 to 11 kg/tU, corresponding to a residual enrichment of 0.9 to 1.1%.

How is Pu-239 produced in a reactor?

Pu-239 is produced when U-238 captures a neutron (U-238 + n to U-239 to Np-239 to Pu-239). In a typical LWR, about 0.15 to 0.20 kg of net Pu-239 is retained in spent fuel per ton of uranium per 1000 MWd/tU of burnup. Pu-239 also fissions and contributes 25 to 35% of total fission power at typical burnup levels.

What is specific power in nuclear engineering?

Specific power (kW/kgU) is the thermal power per unit mass of uranium fuel. It equals the overall thermal power divided by the total fuel loading. Typical PWRs operate at 33 to 38 kW/kgU. Higher specific power means faster burnup but also higher fission product buildup rates and greater mechanical stress on the fuel.

What is a capacity factor in the burnup equation?

The capacity factor is the fraction of time the reactor operates at full rated power over a given period. A capacity factor of 85% means the reactor generated 85% of the energy it would have produced running continuously at full power. It accounts for refueling outages, maintenance, and unplanned shutdowns.

Why does burnup matter for nuclear fuel economics?

Higher burnup means more energy per fuel assembly, reducing the frequency of refueling outages and lowering fresh fuel procurement costs. It also reduces the volume of spent fuel per unit of electricity generated. However, higher burnup requires higher initial enrichment and more radiation-resistant cladding materials.

📌 Quick Tips

💡Typical LWR discharge burnup is 33,000 to 55,000 MWd/tU. Higher burnup reduces fuel costs but requires higher initial enrichment to maintain criticality.

💡Capacity factor accounts for planned and unplanned outages. Most nuclear plants operate at 85 to 92% capacity factor over a year.

💡Increasing burnup from 33,000 to 55,000 MWd/tU reduces the amount of spent fuel per unit of energy produced by about 40%.

💡A Pu contribution of 27 to 35% is typical for PWR fuel at moderate burnup. At very high burnup (above 50,000 MWd/tU), Pu contributes 40% or more of total fission power.

💡The specific power (kW/kgU) is a reactor design parameter. Modern PWRs operate at 35 to 40 kW/kgU, while research reactors can exceed 400 kW/kgU.