The figure represents a hefty increase on the £2 billion loss the lender reported last year and is one of the group’s biggest since its Government bailout in 2008.
The lender, which is 72% owned by the taxpayer, has been stung by billions in restructuring, conduct and litigation charges.
Today’s figures take into account £10 billion in legacy costs, including £5.9 billion on conduct charges and a £2.1 billion restructuring hit.
The group revealed recently it had set aside another £3.1 billion ahead of an expected fine from US authorities - linked to the sale of mortgage-backed securities - which was included in the bank’s results.
RBS has now notched up losses totalling more than £50 billion over the past eight years.
To compound matters, chief executive Ross McEwan has ordered a £2 billion cost-cutting drive, expected to result in the loss of thousands of jobs.
It will include £750 million of savings in 2017.
Mr McEwan said: “The bottom-line loss we have reported today is, of course, disappointing but, given the scale of the legacy issues we worked through in 2016, it should not come as a surprise.
“These costs are a stark reminder of what happens to a bank when things go wrong and you lose focus on the customer, as this bank did before the financial crisis.”
But Mr McEwan said he expects the bank to be profitable by 2018, and pointed to its underlying adjusted operating profit of £4.2 billion, which strips out exceptional charges.
“We made good progress throughout 2016 against our strategy. Our core business generated £4.2 billion in adjusted pre-tax operating profit for the year - that’s an average of £1 billion per quarter for the last eight quarters,” he said.
“We were the fastest growing large bank in the UK last year, with £24 billion of new lending into the economy supporting over a million businesses and home owners.
“This bank has great potential. We believe that by going further on cost reduction and faster on digital transformation we will deliver a simpler, safer and even more customer-focused bank.”
The result comes a week after the Treasury proposed a plan to abandon the sale of RBS’s Williams & Glyn branch network, which will cost the lender £750 million.
The bank had been required to offload Williams & Glyn by the end of the year as part of EU conditions on its £45 billion bailout at the height of the financial crisis.
The lender has struggled to offload the branches, which it was required to do by the end of the year under state aid rules.