Heat Sink Calculator

Heat Sink Calculator finds the thermal resistance in °C/W that a part needs from its power, junction limit and ambient, then sizes a flat plate or a finned heat sink for still air.

Heat Sink Calculator Formula and Inputs

A heat sink is a piece of metal that carries heat away from a transistor, regulator or LED and hands it to the air. The Heat Sink Calculator finds how good that metal has to be. Its answer is a thermal resistance in °C/W, where a lower number means a bigger or better heat sink.

Heat leaves the silicon through three resistances in a row. RθJC runs from the junction to the case, RθCS from the case to the heat sink, and RθSA from the heat sink to the air. Texas Instruments gives the heat sink calculation formula in its application report Understanding Thermal Dissipation and Design of a Heatsink.

$$R_{\theta SA}=\frac{T_J-T_A}{P}-R_{\theta JC}-R_{\theta CS}$$

TJ is the maximum junction temperature and TA is the hottest air the part will sit in. P is the power dissipated in watts, usually voltage across the part times the current through it. The Electrical Power Calculator gives that wattage when only volts and amps are known.

The Heat Sink Calculator opens on 10 W, a 150 °C junction limit, 40 °C air, 3 °C/W junction-to-case and 1 °C/W case-to-sink. The budget is 110 °C ÷ 10 W, or 11 °C/W. Taking away 3 and 1 leaves 7.00 °C/W, so any heat sink rated 7 °C/W or lower holds the limit.

A thinner interface changes the answer. With the case-to-sink figure cut to 0.1 °C/W for a good grease joint, the same part allows 7.9 °C/W. The Results by Ambient Temperature panel shows the other direction, where 60 °C air drops the allowance to 5.00 °C/W and 85 °C air to 2.50 °C/W.

Junction Temperature and Maximum Power

The Calculate menu of the Heat Sink Calculator turns the same chain around three ways. Junction Temperature adds the resistances and multiplies by the power, which makes the tool a heat sink thermal resistance calculator run in reverse.

$$T_J=T_A+P\times (R_{\theta JC}+R_{\theta CS}+R_{\theta SA})$$

With a 5 °C/W heat sink the total is 9 °C/W, so 10 W lifts the junction 90 °C above the air. At 40 °C ambient that is 130 °C, which sits 20 °C under the limit. The case runs at 100 °C and the heat sink temperature is 90 °C, 50 °C above the air around it.

Those two figures can be checked with a thermocouple on a finished build. The first card shows the bare package. With a junction-to-air figure of 62.5 °C/W and no heat sink, 10 W would put the junction at 665 °C, which no part survives.

$$P_{MAX}=\frac{T_J-T_A}{R_{\theta JC}+R_{\theta CS}+R_{\theta SA}}$$

Maximum Power divides the temperature budget by the total resistance. The 5 °C/W heat sink allows 12.22 W, against 1.76 W for the bare package. Each extra degree of ambient removes 0.111 W, so 50 °C air allows 11.11 W and 30 °C air allows 13.33 W.

What Size Heat Sink Do I Need?

A °C/W figure is enough to shop a catalog, but it does not say how big the metal is. The Heat Sink Calculator turns the required rating into two sizes, a flat plate and a finned extrusion, and both are given in mm and cm². That makes it a heat sink calculator in metric units, with an inch option for the fin dimensions.

The flat plate heat sink calculator card uses a rule of thumb from Rod Elliott's heatsink article at Elliott Sound Products. Thermal resistance is about 50 divided by the square root of the plate area in square centimeters.

$$A={\left(\frac{50}{R_{\theta SA}}\right)}^2$$

For 7.00 °C/W the area is 51.0 cm², a square plate 71.4 mm on a side or 7.91 in². Elliott's own example is a 100 cm² plate for about 5 °C/W. Area grows with the square of the improvement, so halving the rating to 3.5 °C/W needs four times the plate, 204 cm².

The finned card answers the same question for an extrusion standing in open air. For the default part it gives 4 fins on a base 23.9 mm wide, with a 6.0 mm gap between fins. That profile is 75 mm long and 25 mm high, and it rates 6.21 °C/W because the fin count rounds up.

Heat Sink Calculator for a MOSFET

A MOSFET that is fully on dissipates its drain current squared times its on resistance. The current and resistance follow Ohm's law, and for a switching load the current is the RMS value.

$$P=I^2\times R_{DS(on)}$$

The Vishay IRF540 data sheet lists 0.077 Ω on resistance, a 175 °C junction limit and three thermal figures for the TO-220 package. Junction-to-case is 1.0 °C/W, case-to-sink is 0.50 °C/W on a flat greased surface, and junction-to-ambient is 62 °C/W.

At 8 A the loss is 64 × 0.077, or 4.93 W. With no heat sink in 40 °C air the junction would reach 345.5 °C. The required rating is 135 ÷ 4.93 - 1.0 - 0.5, or 25.9 °C/W, which a 3.7 cm² plate meets. On a 5 °C/W heat sink the junction runs at 72 °C.

Whether a MOSFET needs a heatsink depends on the bare-package limit. For the IRF540 at 40 °C that limit is 135 ÷ 62, or 2.18 W, which is about 5.3 A. At 5 A the loss is 1.93 W, the junction sits at 159.4 °C, and the Heat Sink Calculator reports No Heat Sink Needed. On resistance climbs as the junction heats, so real loss runs above the 25 °C figure.

Natural Convection Fin Design

To design a heat sink for still air, switch the menu to Heat Sink Size and Fin Count. That mode is a heat sink calculator for natural convection. It takes the power, the ambient temperature and the hottest the heat sink may get, then designs a vertical plate-fin profile from the length, height, base and fin thickness entered.

The first step is the fin gap. Fins set too close choke the rising air between them, and fins set too wide waste base width. The optimum spacing depends on the fin length and the temperature rise.

$$s=2.71\times {\left[\frac{g\beta (T_S-T_{AMB})}{L\alpha \nu }\right]}^{-1/4}$$

Here g is gravity, β is one over the average air temperature in kelvin, α is the thermal diffusivity of air and ν is its kinematic viscosity. The Heat Sink Calculator then adds convection and radiation from the two outer faces and from each fin channel until the total covers the load.

$$W=(N-1)\times s+N\times t$$

For 10 W, 40 °C air and a 100 °C heat sink, the result is 5 fins at 6.1 mm spacing on a base 31.9 mm wide. Convection sheds 7.93 W and radiation 3.23 W, a capacity of 11.15 W. The needed rating is 6.00 °C/W and the size shown rates 5.38 °C/W.

Radiation carries 29% of that load. Texas Instruments puts radiation at roughly 25% of the total in natural convection, so the surface finish matters. Dropping the emissivity entry from 0.85 to 0.05 raises the same design to 7 fins and 47.1 mm.

The table holds 10 W and a 100 °C heat sink while the air warms. A heat sink that is 31.9 mm wide in a 40 °C room must be 249.3 mm wide inside an 85 °C enclosure. The last card lists 52.8 g of aluminum, a 59.8 cm³ outline and 165 cm² of fin surface for the 40 °C design.

The method assumes the heat source covers the whole base, with fins vertical in open air. A small TO-220 tab on a wide base runs hotter than the figure shown. Elliott notes that fins laid horizontal lose a large share of their cooling, so a first size from this mode needs margin.

Forced Convection and Fans

The series formula does not change with a fan. The required RθSA is still 7.00 °C/W for the default part, so the first three modes serve as a heat sink calculator for forced convection as well. What changes is the size of metal that reaches the rating.

Catalog heat sinks list two ratings, one in still air and a curve against air speed. Enter the forced-air figure from that curve in the Heat Sink Calculator as Your Heat Sink Rating to test it. The fin count and plate area cards assume still air and oversize a fan-cooled part.

Robert Simons models the fan-cooled case in Electronics Cooling. Resistance falls as the heat transfer coefficient, fin count and fin efficiency rise.

$$R_{HS}=\frac{1}{h\times (A_{BASE}+N\times \eta \times A_{FIN})}$$

His 50 × 50 mm aluminum example shows the limit of that approach. Past a certain fin height and fin count the gain flattens, because packed fins raise the pressure drop and the fan moves less air. The heat sink and the fan curve have to be matched together.

How to Apply a Heat Sink

The joint between case and heat sink is the one resistance set on the bench. Elliott's table for a TO-220 lists 1.1 to 1.3 °C/W mounted dry, 0.9 to 1.1 with grease, 1.0 to 1.6 for mica with grease and 1.5 for a silicone pad. A TO-3 case with grease is 0.3 to 0.5 °C/W.

In the Heat Sink Calculator, each 0.5 °C/W across that joint costs 5 °C at the junction at 10 W. Spread a thin film of grease, tighten the screw to the data sheet torque and stand the fins vertical. An insulating pad is needed whenever the tab is live and the heat sink is grounded.

Selecting a heat sink then comes down to four checks. The catalog rating is at or under the RθSA from the Heat Sink Calculator at the real air speed. The part fits the board and the mounting hole. The junction lands well under the data sheet limit, and the enclosure air is the ambient used in the math.

A good heat sink is one that clears the required rating with room to spare, and sometimes that is none at all. The 1.21 W lost in the Flyback Switch Mode Regulator Calculator example sits under the 1.76 W bare-package limit. The 12.22 W case needs 5 °C/W, which the plate rule puts at 100 cm² of aluminum.

Types of Heat Sinks

Heat sinks are grouped by how they are manufactured. Celsia's guide to heat sink types describes extruded parts as the most cost-effective, with limited design freedom unless they are machined afterward.

Skived fins are cut from a solid block and give thin fins with a high aspect ratio, though the fins bend easily. Zipper fins pack thin sheet-metal fins densely and pair with heat pipes. Bonded fin parts suit very large heat sinks and allow a base and fins of different metals.

Die cast parts are limited to thicker fins and suit enclosure covers cooled by natural convection. Forging and CNC machining allow intricate shapes at higher cost. Celsia rates aluminum at about 200 W/m-K and copper at about 400 W/m-K, so copper spreads heat twice as well at a higher weight and price. Whichever type is chosen, the °C/W from the Heat Sink Calculator is the figure to match on its data sheet.

Heat Sink Calculator Excel Formulas

A heat sink calculator in Excel needs seven entries and seven formulas. The cells below reproduce the Heat Sink Rating mode, with temperatures in °C, resistances in °C/W and plate area in cm².

Filling column B down a list of ambient temperatures rebuilds the ambient table. The fin count is harder to copy into a sheet, because the air properties change with temperature and the spacing formula needs them at each step.

Heat, Watts and Joules

How do you calculate heat flow and heat rate?

Heat flow through a heat sink is the temperature difference divided by the thermal resistance. A 7 °C/W heat sink that runs 70 °C above the air passes 10 W. The unit of heat rate is the watt, which is one joule per second, and the SI unit of heat itself is the joule.

A joule is not equal to a kilowatt, because one is energy and the other is power. One kilowatt is 1,000 joules every second. The 10 W in the default example is 0.01 kW, so it sheds 40 joules in 4 seconds, 200 joules in 20 seconds and 300 joules in 30 seconds.

In electrical terms 300 joules is 300 watt-seconds, or 0.0000833 kWh. The Electrical Energy Calculator converts power and time to energy, and the Energy Consumption Calculator prices it in kWh.

What is the formula to calculate heat?

The heat needed to warm a mass is the mass times its specific heat times the temperature rise. That formula sets how long a heat sink takes to warm up, while the °C/W rating sets where it settles.

$$Q=m\times c\times \Delta T$$

The Heat Sink Calculator lists 52.8 g of aluminum for the natural convection example, and aluminum has a specific heat near 0.9 J/g·°C. Warming it 60 °C stores about 2,850 joules. At 10 W that takes at least 285 seconds, which is why a short power pulse runs cooler than the steady-state figure.

What are the three methods of heat transfer?

The three are conduction, convection and radiation, and a heat sink uses all of them. Conduction carries heat from the junction through the case, the grease and the aluminum. Convection hands it to moving air, and radiation sends the rest to the surroundings as infrared.

In the 10 W fin design from the Heat Sink Calculator, convection removes 7.93 W and radiation 3.23 W. A fan raises the convection term while radiation stays the same, so finish matters less under forced air. Conduction is why a thick base and a flat mounting face lower the junction temperature.

How is the size of a heat exchanger calculated?

A heat exchanger is sized by area. The duty in watts is divided by the overall heat transfer coefficient and the log mean temperature difference between the two fluids.

$$A=\frac{Q}{U\times \Delta T_{LM}}$$

A heat sink is the same calculation with air on one side only. One over the thermal resistance equals U times A, so a 7 °C/W heat sink has a conductance of 0.143 W/°C. The 5.38 °C/W fin design above reaches 0.186 W/°C with coefficients of 6.3 and 7.6 W/m²·K on its surfaces.