library(shiny)

ui <- fluidPage(
  numericInput("temp_c", "Celsius", NA),
  numericInput("temp_f", "Fahrenheit", NA)
)

server <- function(input, output, session) {
  c_to_f <- function(c, decimals = 1) {
    round((c * 9 / 5) + 32, decimals)
  }

  f_to_c <- function(f, decimals = 1) {
    round((f - 32) * 5 / 9, decimals)
  }

  observeEvent(input$temp_c, {
    # This early return is to prevent event handler cycles.
    # For example, setting F to 40 sets C to 4.4, which sets F to 39.9.
    # The conditional here is a crude way to prevent that 39.9.
    if (isTRUE(input$temp_c == f_to_c(input$temp_f))) {
      return()
    }
    updateNumericInput(session, "temp_f",
      value = c_to_f(input$temp_c))
  })

  observeEvent(input$temp_f, {
    if (isTRUE(input$temp_f == c_to_f(input$temp_c))) {
      return()
    }
    updateNumericInput(session, "temp_c",
      value = f_to_c(input$temp_f))
  })
}

shinyApp(ui, server)