PCB Trace Resistance Calculator January 24, 2006
This online web calculator finds the resistance of copper PCB traces (a.k.a. tracks) of given width, thickness, length, and temperature. It can also be used for copper bars (e.g. bus bars). Several choices of common units are available. Enter the Width and Thickness below. Optionally, enter the Temperature and Length, or just leave the default values. (To find the needed trace width based on current, see the PCB Trace Width Calculator.)
May 17, 2006 - Added (lateral) thermal resistance calculations.
January 18, 2007 - Clarified equations.
Tips:
- Resistance per foot can be calculated by entering a length of 1 foot.
- If cookies are enabled, the form will return to its previous state upon your next visit, so your unit preferences etc. will persist.
Required Inputs:
| Width | ||
| Thickness |
Optional Inputs:
| Temperature | ||
| Length |
Electrical Results:
| Resistance | Ohms |
Thermal Results:
| Thermal Resistance | Deg. C/Watt |
Notes:
Electrical Equations:
Resistance = Resistivity*Length/Area*(1 + (Temp_Co*(Temp - 25))
Where, Area = Thickness*Width
A copper Thickness of 1 oz/ft^2 = 0.0035 cm
Copper Resistivity = 1.7E-6 ohm-cm
Copper Temp_Co = 3.9E-3 ohm/ohm/C
Thermal Equations:
Thermal_Resistance = Thermal_Resistivity*Length/Area
Copper Thermal_Resistivity = 0.249 cm-K/W (at 300K)
- Posted in : Calculators, Electrical Engineering, PCB
- Author : Brad
Comments
Thanks for a great, truly useful tool!
A truly useful and easy to use tool! Should have been around a long time ago - thanks!!
Thermal resistance calculations were added at the request of one of our users. This allows calculating the temperature drop along the copper trace if the thermal heat flow (in Watts) is known and assuming all the heat is flowing in the copper.
[…] I had a request to calculate the thermal resistance of a PCB trace, so I updated the trace resistance calculator to add this feature. […]
Hi !
Very interesting site for the entire electronics design/ manufacturing industry. Very useful tools !
I will definately list this site to Links/Resouces page on our site www.PCBindia.com - the eMarket for electronics manufacturing industry.
Thanks a lot for your services to the industry.
Nitin Raulji
CEO
www.PCBindia.com
I don’t have access to…
[Admin] This comment was moved to:
http://circuitcalculator.com/wordpress/2006/01/31/pcb-trace-width-calculator#121
it’s really useful for solving hardware related probs.
thanks !
is there an existing formula for calculating power pin wagon wheel spoke resistance with dimensions: L=5mil W=5mil Thickness=1mil
Kevin,
The formulas and calculator above should do the trick. The result for L=5mil W=5mil Thickness=1mil is 0.000669 Ohms at 25 degrees C.
Brad
I’m getting two different answers. I’m calculating the resistance of a trace of 1oz copper. In the table above I enter: Width = 4mm, Thickness = 1oz/ft^2, Length = 376.15mm; Total R=45.7mOhms.
This is good.
By hand calculation: [Rho(Ohm.M)xLength(M)]/[A^2(M^2)]. I get 42microOhms. I must not be applying my units correctly. Any help?
Thanks, Brian
Brian,
Thanks for the question. I think you may have used a wrong conversion factor. In reviewing the notes below the calculator, they were not very clear, so I added this to the post:
Where, Area = Thickness*Width
A copper Thickness of 1 oz/ft^2 = 0.0035 cm
Then, in your example you get:
Resistance = Resistivity*Length/Area
Resistance = Resistivity*Length/(Thickness*Width)
(1.7E-6 ohm-cm)*(376.15 mm)/{(0.0035 cm)*(4 mm)}
(I left length and width in mm because the units cancel.)
Resistance = 0.0457 Ohms
I hope that helps,
Brad
How do I calculate the PCB copper area needed to cool a DPAK or other package?
Magnus,
See the Zoho spreadsheet in the post here:
http://circuitcalculator.com/wordpress/2007/02/16/pcb-thermal-copper-area/
Brad
Great program!
Bulk resistivity of pure copper is 6.58E-07 ohm-inch
Bulk resistivity of copper wire & trace is 6.787E-07 ohm-inch
due to annealing and impurities…
from
Dr. Howard Johnson’s website
http://www.sigcon.com/lib/htm/RESIST.htm
Hi Richard,
Thanks for the information. For the sake of comparison, I converted the numbers from Dr. Johnson’s website to ohm-cm and got:
Bulk resistivity of pure copper is 1.67E-07 ohm-cm
Bulk resistivity of copper wire & trace is 1.72E-07 ohm-cm
The number I have been using for the resistivity of traces (1.7E-6 ohm-cm) appears to be the same to 2 significant figures with a discrepancy of only 1.4%. I have also seen slightly different numbers so I am hesitant to use 3 significant figures.
By the way, Dr. Johnson web site is excellent!
Brad
Can we calculate the capacitance of the PCB trace ? If yes then please also post the PCB trace capacitance calculator.
Rajiv,
See:
http://circuitcalculator.com/wordpress/2007/03/06/transmission-line-calculator/
Brad
I wonder how the Thermal resistance goes up in value if the trace length is higher? You would think the opposite is true. the more area the less the Thermal Resistance.
Ray,
To clarify, the thermal resistance calculated above is for heat conducted laterally along the length of the trace, so the longer the trace, the higher the thermal resistance. (See lateral heatflow on page 14 of [1] below.)
It is NOT calculating the thermal resistance of, say, an external trace to the ambient air (which DOES go down as area goes up as you described). This type of thermal resistance is discussed on page 13 of [1]. My calculator in reference [2] deals with the thermal resistance to ambient.
[1] “Constructing Your Power Supply - Layout Considerations”, by Robert Kollman
http://focus.ti.com/lit/ml/slup230/slup230.pdf
[2] http://circuitcalculator.com/wordpress/2007/02/16/pcb-thermal-copper-area/
Great calculator for conducted thermal resistance.
Any info on how tin plating might change the thermal resistance? Rather than use 2 ounce copper, I am thinking about having areas like pads (no soldermask) so it gets tin plated. A secondary idea is to place pads in the paste stencil so these areas get extra solder thinkness to boot. I have found that I need to spread heat away from a DPAK faster than standard SMOBC allows. I figure that making a “rib” of solder may allow the heat to get to the far edges of the copper heat pad quicker (2 inches away), possibly doing this with multiple vias as well.
Charlie,
While adding tin and/or solder will help a little, copper has a thermal conductivity 6 times better than tin and 10 times better than solder. So, your best bet is probably to add copper. Tin plating is also usually very thin and is just done to protect the copper from oxidation and improve solderability. Copper on the other hand may be plated up an ounce per square foot or more.
Brad
Thanks Brad, I knew copper was superior but didn’t realize that it was that extreme.
I am trying to get 6 or 7 Watts of heat out of a DPAK. Using the thermal resistance calculator (above), it seems I can lose all hope if my heatsink isn’t very close to the DPAK. For, if you figure, 1oz copper and about .25 inch on three sides of the DPAK to transfer heat, if an ideal heatsink were only 0.1 inch away on three sides, temp diff across the .1 inch is 9.5C/W x 7W or 66C. If I am thinking about this right (let me know), going to 2oz will reduce that to 33C and if I can also bring the heatsink to .05 inches, then down to 17C. And, to achieve this, probably requires a custom tin plated copper heatsink, surface mounted with exact placement. With my current heatsink that is rated at 14C/W, I only have one side exposed to the heatsink which puts me at 28C/W for the transfer from DPAK to heatsink, which yeilds an effectiveness of 28+14 or 42C/W.
Thanks again.
Thanks for the Calculator…
Its really helpful for me…
Can you help me regarding thermal model for trace and via?
Thanks Darshan. I will email you regarding the thermal model.
A very quick and helpful tool. It is in my favorite folder and I often use it when I need a quick calculation of PCB trace resistance.
It should be useful to calculate trace inductance too…
Ivan,
Inductance requires a few more input parameters, so I have a separate calculator:
http://circuitcalculator.com/wordpress/2007/03/06/transmission-line-calculator/
Brad
Thanks Mingkai!
Brad
Thanks for having that tool.
Planes will fly better now:)
If I am measuring resistance (very low resistance on milliOhm range) on connectors (for example board to board connector), which are placed in the center of a PCB with some traces (trace is probably .5in) leading to test points to probe to (sourcing current on a pair and measuring voltage on another pair). Is there something I need to consider regarding the trace’s shape and length? Signals to be used are 100mA-50Amps DC and at some point 600Hz 100nA pp signal AC. Do you have any books/links that would help?
Gina,
I’m not sure I understand exactly what you are doing, but it sounds like the resistance measurement could be affected the uniformity of the current distribution. Some key word to search on would be “4 wire resistance measurement uniform current”.
I found the following page that may be of interest:
http://www.qdusa.com/resources/pdf/ppmsappnotes/1076-304.pdf
Thanks! I will take a look at the document. I am trying to take low resistance measurements on connectors by supplying the current and measuring voltage. I need to control the current therefore I am not using an Ohmmeter that has a 4wire option.