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Sure - we can run through a simple calculation based on that.
The only number that we need for the beam calc is the pound force on the beam and the length of the beam
You have defined that as 200 lbs/ft and 84 inches
2x8 lumber.
1.5" x 7.25" nominal (less when fully dry, sadly)
Moment of inertia for a solid rectangle with a vertical force
Iy = height * width^3 / 12
l = 47.63 in4
Young's Modulus
SPF #2 lumber - properly graded and avg. moisture content using NLGA.ORG values with no modifier for moisture or other factors.
E = 1,400,000 PSI
84 Inch Span
L = 84
200 lbs/ft - we are working in inches (PSI for Young's and in4 for Inetrtial Moment) so we need to convert
w = 16.67 lbs/in
Simply support beam with uniform load
Formula to apply for bending moment, solving for deflection.
Deflection = (5 * 16.67 * 84^4) / (384 * 14000000 * 47.63)
Max Deflection at center of span = .16 inches
Hope that helps a bit. I am not sure of that matches the calculator that you listed or not, but I am confident in the formulae that I have applied given your constraints.
Please excuse unit symbolization - don't have easy access to formatters for this type of math and symbol sets right now.
0.16 vs 0.146 (0.15)