Thermal Resistance Network Calculator
Calculate equivalent thermal resistance for series paths, parallel heat-flow paths, series temperature drops and a simple series-parallel thermal network. THM-003 is intended for package, interface, PCB, heatsink, chassis and shared cooling approximations when each path can be represented as a lumped Rθ.
This tool is different from a single equivalent-Rθ temperature calculator and from a fixed heatsink path calculator. It is a generic steady-state network solver and does not replace transient thermal impedance, airflow, spreading-resistance, FEA or measured thermal validation.
Engineering tool
Thermal Resistance Network Calculator
Calculate equivalent thermal resistance for series, parallel, and simple series-parallel thermal paths.
Select the unit used by every network resistance row.
Reference temperature used to report the hot-side temperature.
Steady-state heat flow through the equivalent network.
Series Thermal Path
Result console
- Equivalent Thermal Resistance
- 5°C/W
- Total Temperature Rise
- 50°C / K rise
- Hot-Side Temperature
- 75°C
- Rθ1 Drop
- 10°C / K rise
- Rθ2 Drop
- 5°C / K rise
- Rθ3 Drop
- 35°C / K rise
Series elements carry the same heat flow; higher resistance elements create larger temperature drops.
Formula
Formula reference
Thermal resistance network formulas
Series paths add by resistance. Parallel paths add by conductance because each branch sees the same temperature difference.
Series: Req = ΣRiParallel: 1 / Req = Σ(1 / Ri)Conductance: Gi = 1 / RiSeries drops: ΔTi = P RiParallel total heat: ΔT = Ptotal ReqParallel branch heat: Pi = ΔT / RiParallel fraction: Pi / Ptotal = Gi / ΣGiMixed: Req = Rbefore + Rparallel + RafterEquivalent rise: ΔT = P ReqHot side: Thot = Tref + ΔTVariable definitions
- Req
- equivalent thermal resistance
- Ri
- individual thermal resistance
- Gi
- thermal conductance
- P
- heat flow through a series or equivalent network
- Pi
- branch heat flow
- ΔT
- temperature difference
Thermal Network Formula Audit
| Adopted Network Model | Steady-state lumped thermal resistance network. |
|---|---|
| Series Formula | Req = ΣRi. |
| Parallel Formula | 1/Req = Σ(1/Ri). |
| Conductance Formula | Gi = 1/Ri. |
| Series Temperature Drop Formula | ΔTi = P Ri. |
| Series Conservation Check | ΣΔTi = P Req. |
| Parallel Temperature Difference Formula | ΔT = Ptotal Req. |
| Parallel Branch Heat Formula | Pi = ΔT / Ri. |
| Parallel Fraction Formula | Pi / Ptotal = Gi / ΣGi. |
| Parallel Conservation Check | ΣPi = Ptotal. |
| Mixed Topology | Req = Rbefore + Rparallel + Rafter. |
| Equivalent Rise Formula | ΔT = P Req. |
| Hot-Side Temperature Formula | Thot = Tref + ΔT. |
| Series Zero-R Policy | Zero-valued series elements are allowed as ideal segments. |
| Parallel Zero-R Policy | Zero-valued parallel branches are rejected to avoid infinite conductance. |
| Negative Resistance Policy | Negative thermal resistance is rejected. |
| Temperature Difference Convention | °C difference and K difference are numerically equal. |
| Absolute Temperature Convention | Absolute temperature inputs are converted to °C internally. |
| Steady-State Boundary | No thermal capacitance, transient impedance or time constant model. |
| Geometry Boundary | Package spreading, TIM geometry and airflow are entered as known resistances. |
Worked Examples
| Input | Calculation | Result |
|---|---|---|
| Series R = 1, 0.5, 3.5 | Req = 1 + 0.5 + 3.5 | 5°C/W |
| Series P = 10 W | ΔT drops = 10, 5, 35 | 50°C total |
| Series Tref = 25°C | Thot = 25 + 50 | 75°C |
| Parallel R = 10 and 20 | Req = 1 / (0.1 + 0.05) | 6.6667°C/W |
| Parallel Ptotal = 3 W | ΔT = 3 × 6.6667 | 20°C |
| Parallel branch A | P1 = 20 / 10 | 2 W |
| Parallel branch B | P2 = 20 / 20 | 1 W |
| Parallel fractions | 2/3 and 1/3 | 66.67% and 33.33% |
| Parallel equal branches 10 and 10 | Req = 10 / 2 | 5°C/W |
| Three equal 30°C/W branches | Req = 30 / 3 | 10°C/W |
| Mixed network | 1 + (6 || 3) + 0.5 | 3.5°C/W |
| Mixed with P = 10 W | ΔT = 10 × 3.5 | 35°C |
| Equivalent rise | Req = 5°C/W, P = 10 W | 50°C |
| Equivalent hot side | Tref = 25°C, ΔT = 50°C | 75°C |
| Conductance of 10°C/W | G = 1 / 10 | 0.1 W/K |
| Conductance of 20°C/W | G = 1 / 20 | 0.05 W/K |
| 1 K/W | thermal resistance difference scale | 1°C/W |
| 9°F/W | 9 × 5/9 | 5°C/W |
| 90°F temperature difference | 90 × 5/9 | 50°C |
| Zero series element | 0 + 2 | 2°C/W allowed |
| Zero parallel element | 1 / 0 conductance | Rejected |
| Negative resistance | Ri < 0 | Rejected |
| Empty series network | no elements | Rejected |
| Single parallel branch | minimum branches not met | Rejected |
| Parallel conservation | 2 W + 1 W | 3 W total |
| Series conservation | 10°C + 5°C + 35°C | 50°C total |
| Very small positive branch | finite positive R | Handled without NaN |
| Very large finite branch | finite positive R | Handled without Infinity |
Engineering Notes
Thermal Resistance Network
A thermal network represents heat-flow paths as lumped resistances.
Series Thermal Resistance
Series elements share the same heat flow and add directly.
Parallel Thermal Resistance
Parallel paths share the same temperature difference and combine by conductance.
Equivalent Thermal Resistance
Req replaces the modeled network when only total heat flow and total temperature rise are needed.
Thermal Conductance
Conductance is 1/Rθ and determines heat-flow sharing in parallel branches.
Heat Flow
Heat flow is the thermal power moving through the modeled path.
Temperature Drops
Each series element creates a drop proportional to its resistance.
Energy Balance
In steady state, branch heat flows must sum back to total heat flow.
Steady-State Lumped Model
This calculator ignores time, thermal capacitance and geometry-dependent spreading.
Thermal Path
Use realistic path definitions such as junction, case, pad, PCB, chassis, sink and ambient.
PCB Paths
Board copper and thermal vias can be represented as known lumped paths if the approximation is valid.
Shared Sink Paths
Parallel branches are useful when heat splits between a heatsink and a PCB or chassis path.
Model Boundary
Do not treat a network result as a substitute for detailed CFD, FEA, SPICE thermal models or measurement.
Common Mistakes
- Adding parallel thermal resistances directly instead of adding conductances.
- Distributing parallel heat flow by resistance instead of conductance.
- Assuming every branch carries equal heat flow when branch resistances differ.
- Using a zero-resistance parallel branch and accepting Infinity as a result.
- Using negative thermal resistance values.
- Mixing absolute temperature with temperature difference units.
- Adding RθJA to a network that already includes junction-to-ambient paths.
- Treating a steady-state thermal network as a transient thermal simulation.
- Ignoring contact, spreading, airflow or mounting conditions behind entered resistance values.
- Forgetting that branch heat flows must sum to the total heat flow.
- Using electrical input power instead of actual heat loss.
- Modeling complex 3D heat spreading as a simple network without margin.
Support reference
FAQ
What is a thermal resistance network?
A thermal resistance network is a lumped steady-state model that represents heat-flow paths using thermal resistance values in °C/W or K/W.
How do series thermal resistances combine?
Series thermal resistances add directly: Req = R1 + R2 + R3. The same heat flow passes through every series element.
How do parallel thermal resistances combine?
Parallel thermal resistances combine by conductance: 1/Req = 1/R1 + 1/R2 + 1/R3.
Why does parallel heat flow use conductance?
Parallel branches share the same temperature difference, so branch heat flow is ΔT/Ri. Lower resistance means higher conductance and more heat flow.
Can thermal resistance be zero?
A zero series resistance can be used as an idealized segment. Zero resistance in a parallel branch is rejected because it would create infinite conductance in this model.
Can thermal resistance be negative?
No. Negative thermal resistance is not valid for this steady-state passive network calculator.
What is equivalent thermal resistance?
Equivalent thermal resistance is the single Rθ value that produces the same temperature rise for the same total heat flow as the modeled network.
How do I calculate temperature rise from thermal resistance?
Use ΔT = P × Req, where P is heat flow in watts and Req is equivalent thermal resistance in °C/W or K/W.
How do I calculate branch heat flow in parallel paths?
First calculate the common temperature difference, then use Pi = ΔT/Ri for each branch.
What is thermal conductance?
Thermal conductance is the inverse of thermal resistance: G = 1/Rθ. Parallel heat-flow calculations are easiest using conductance.
Does this calculator model transient thermal impedance?
No. THM-003 is a steady-state lumped thermal resistance calculator and does not model thermal capacitance or Zθ(t).
Does this calculator model contact spreading resistance?
No. Enter each thermal resistance as a known value. Detailed interface, spreading and geometry effects are outside V1.
Can I model a package, thermal pad, heatsink and PCB path together?
Yes, if each part can be represented as a lumped resistance and the topology fits series, parallel, or the simple series-parallel mode.
What is the difference between THM-003 and THM-001?
THM-001 uses one known equivalent resistance. THM-003 calculates the equivalent resistance from multiple network elements.
What is the difference between THM-003 and THM-002?
THM-002 uses a fixed heatsink path RθJC + RθCS + RθSA. THM-003 is a generic thermal network calculator for series, parallel and mixed paths.
Can a parallel thermal path have only one branch?
No. A parallel network needs at least two positive-resistance branches. Use series or equivalent-rise mode for one path.
Are °C/W and K/W equivalent?
Yes. For thermal resistance and temperature difference, 1°C/W equals 1 K/W.
Can I use °F/W?
Yes. The calculator converts °F/W to °C/W internally using the temperature-difference scale.
Does lower thermal resistance always carry more heat in parallel?
Yes for this steady-state model. Lower resistance has higher conductance, so it carries a larger heat-flow fraction for the same common temperature difference.
Does network resonance or electrical resistance affect this tool?
No. This is a thermal resistance network model, not an electrical circuit, transient thermal simulation, or fluid-flow solver.
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