Date: 201808
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Night
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Cargo / Freight / Delivery
Flight phase: Initial Climb
Airspace: Class B ZZZ
ATC / advisory: TRACON ZZZ
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Commercial; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Human-Machine Interface; Communication Breakdown
Second reporter function: Pilot Not Flying; First Officer
Anomaly: Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft TA; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: On departure from RWY XXL from ZZZ; we were to fly the RNAV departure to ZZZZZ. When we took the runway; I saw ZZZZZ on my lower display screen. We took off and at 400 feet [and] I called for LNAV. Soon after VNAV was engaged; the aircraft turned left. I looked over the yoke to see where the aircraft was headed; I saw ZZZZZ1 as the active waypoint. It was at this time ATC asked if we were turning to ZZZZZ; we said we were flying the departure route. They told us to turn to heading 300; then shortly after; said make an immediate turn to 320 [heading]. I disengaged the autopilot and made a sharp right turn to 320 [heading]; I could see another aircraft off to our left that looked to be somewhere between 500 to 1;000 feet below us. We rejoined the departure route with no other incident. In our turn to the 320 heading; we did receive one traffic warning from our TCAS. This could have been avoided had I not let myself get rushed and double checked the First Officer's FMC route inputs. He had mistakenly put in RWY XYL not RWY XXL; which was our departure runway. I also should have looked over the yoke to make sure of the first point on the RNAV route. I failed to slow down and double check; it is my fault the incident happened.


Second narrative: It was the Captain's leg and we were cleared for takeoff on Runway XXL in ZZZ on the RNAV departure procedure with the appropriate 'ZZZZZ RNAV' phraseology; and had an uneventful takeoff. During climbout; all standard operating procedures were followed and the autopilot was selected to center command for the departure procedure. As we climbed through an altitude of approximately 1;100 feet indicated; ATC questioned if we were in the depicted turn to ZZZZZ; which was the next fix for sequencing in the FMC 'Flight Management Computer.' Simultaneously; while realizing our aircraft track was incorrect; the Tower issued an immediate turn to a heading of 300 degrees. While in the assigned right turn; we received a 'TRAFFIC' annunciation from the aircraft TCASS warning system; and the Tower then issued an immediate turn to a heading of 320. During the additional turn; the Captain selected the autopilot off to provide a better turn radius for the new heading. Once established on this heading and continuing our climb to the depicted altitude of 10;000 feet; the Captain called for the autopilot to again be selected to center command. We were issued a frequency change to the assigned ZZZ Departure frequency; and the new controller provided a number for the Tower to call after landing; based on this course deviation.Once we were at a safe altitude; I began to review the RVAV procedure and all associated inputs in the FMC. I quickly realized that the incorrect runway was line selected; which was Runway XYL instead of the correct runway; XXL. This incorrect runway created the off course path; which required the immediate turn for course correction. In retrospect; the line selection for Runway XXL was very close to Runway XYL; which I completely selected in error; and then with my routine check of all inputted data; I did not identify my error. In addition with all briefings of both graphical and textual data for the departure procedure; the error was not discovered. Also; with runway verification; I did not notice that XYL was depicted in the FMC and on the primary flight display. Having never been in this position before after flying jets for over 18 years; I was completely sick to my stomach with this very simple; but extremely problematic error. At this point going forward; I will be extremely vigilant with runway selection while flying an RNAV procedure at a busy airport with multiple runways utilized for departure. I will also provide an additional check of runway selection in the FMC before positioning on the active runway; and hopefully this will never happen again.


Synopsis: Air carrier flight crew reported improper FMS programing resulted in an airborne conflict.