Every person in Britain will need to pay about £5,000 a year between now and 2050 on rebuilding and using the nation's entire energy system, according to government figures. But the cost of developing clean and sustainable electricity, heating and transport will be very similar to replacing today's ageing and polluting power stations, the analysis finds.

The forecasts come from a unique open-source analysis package, called the 2050 pathways calculator, which was created by Professor David MacKay, chief scientific adviser to the Department of Energy and Climate Change.

The predictions challenge suggestions that the costs of embracing low-carbon energy and meeting the UK's legally binding commitments to tackle global warming will be higher than the bill would be for using traditional energy sources. They are also supported by a major EU project that found developing renewable energy was no more expensive than alternatives.

"The calculator takes the poison out of the debate," MacKay told the Guardian. "The key thing is that any scenario you choose has to add up." He said the tool, constructed with the help of hundreds of experts and a thorough literature review, is used to enable "open source policy making", where anyone can see and challenge the assumptions made and the data used. "You can play at being secretary of state, and you have to make a plan which is not too unpopular."

The calculator was used to create the three scenarios set out in the government's official carbon plan, which shows how the UK could meet its emissions targets by 2050 while keeping the lights on, and to test a "cost-optimised" scenario, ie the cheapest.

Doing almost nothing to develop low-carbon energy systems – and busting the UK's carbon targets – would cost £4,682 a year, spent on imported gas for electricity generation and heating and oil for all vehicles. That is 13% of the expected £35,000 average income over the period. By comparison, the least-cost 2050 scenario is £84 (1.8%) a year less expensive, and envisages a mix of electricity generation comprising 42% renewable energy, 31% nuclear power and 27% gas plants with the carbon captured and stored underground (CCS). It also envisages improvements in energy efficiency, with demand from lighting and appliances having fallen by 60% compared with 2007 levels.

However, the cost of the "do nothing" option does not include the damage to the economy expected as a result of climate change, and the calculator notes that, according to the landmark Stern review: "This is the equivalent of up to £6,500 per person per year on average, on top of the cost of the energy system."

The government's "higher renewables, more energy efficiency" scenario, in which wind delivers 55% of the total electricity supply and all cars and buses are fuelled by batteries or hydrogen fuel cells, is forecast to cost £368 a year (8%) more than the "do nothing" scenario, if climate change damage is ignored.

The "higher CCS, more bioenergy" scenario is £470 (10%) more than doing nothing, and assumes the successful deployment of CCS technology at commercial scale, as well as being used with sustainable and plentiful biomass supplies to generate "negative" emissions.

The final scenario, "higher nuclear, less energy efficiency", is the most expensive, £499 (11%) more than doing nothing.

Some experts argue the analysis cannot take into account key future developments though. Professor Dieter Helm, at Oxford University, is unconvinced that the costs of low-carbon and high-carbon energy scenarios will necessarily prove to be similar. "This [similarity] is indeed the result you get if you take conventional wisdom on fossil fuel prices and assume no major technical progress. But these are precisely the two assumptions which would make a difference." Helm says gas may turn out to be cheap and abundant, but also that technology advances in batteries, the electrification of transport, breathroughs in solar power - such as the harnessing of photosynthesis - and the use of smart grids could cut the costs of low-carbon energy too. "The calculator is very interesting," Helm says. "My own view is that making detailed cost estimates is a heroic and potentially very misleading exercise."The nation's energy use splits roughly into three, MacKay says: transport, heating and electricity. But the biggest costs come from transport, as the "millions of individual, little power stations driving around" – cars and lorries – use energy far less efficiently than large power stations.

The new version of the calculator is the first to include costs, an essential component, says MacKay: "You can't have a grown up conversation about this issue without costs." He says the tool is now being used as the basis for equivalents in China, Portugal and Belgium.MacKay believes the calculator has an essential role to play in assessing the feasibility of different energy choices. He describes the government's current policy of backing multiple technologies as a sensible "hedge". Groups from National Grid to Friends of the Earth have already posted their preferred scenarios on the calculator website.

As an example, MacKay says: "An interesting question is what is the trade-off between energy efficiency and building more generation capacity? Do you want really good retrofits of homes, or just build new nuclear plants. In the calculator, people can choose."

However, he notes that the lowest cost options do involve a very strong effort on increasing energy efficiency and cutting waste, as this is a cheaper overall than building new power stations. Another example, included in the government's Carbon Plan, is "How could the cost of a pathway change if, say, nuclear costs are high and the cost of, say, renewables are as low as credible experts believe is possible?"

Shale gas, which is currently being explored in Lancashire and has driven prices down in the US, is not explicitly included in the calculator. But can be easily incorporated, says MacKay, by choosing a low gas price in the model. There is a possible "positive future" when domestic shale gas cuts prices and CCS is working, he says.

MacKay, a professor of physics at Cambridge University, was appointed to government in 2009 shortly after publishing a surprise bestseller book called Sustainable Energy – Without the Hot Air. "I was irritated by all the twaddle being talked about energy and the misleading comparisons made. I just wanted the numbers without the hype," he said. "I am just the numbers guy, trying to be helpful."

From numbers guy to publishing sensation

"I was distressed by the poor quality of the debate surrounding energy. I was also noticing so much greenwash from politicians and big business. I was tired of the debate – the extremism, the nimbyism, the hairshirt." That, Prof David MacKay told the Guardian in 2009, was why he wrote a book in his spare time called Sustainable Energy – Without the Hot Air. He published it as a free pdf on his website, from where you can still download copies without charge. Yet this expertly written but amateurishly published book has now sold over 40,000 copies in print and been downloaded about 400,000 times. "The Guardian made us a star," he says.

It has also been translated by volunteers into Japanese, German, Spanish, Hungarian, Polish and French. An Australian "translation" also exists, which sets the energy questions in a specifically Australian context. Very few areas have needed changes since, he says now: "The book was mainly about the laws of physics and they have not changed." A reanalysis of the land area needed for wind turbines was an exception, after he was accused of being "anti-wind" and "pro-nuclear", though the numbers changed only a little. He is neither, he said, being "pro-arithmetic" instead.

MacKay, a physics professor at Cambridge University, says he did not write the book to make money. However, it did land him a job: nine months after the book was published, he was appointed chief scientific adviser to the Department of Energy and Climate Change.

• This article was amended on 29th December. The headline was changed to make clear the comparison between the costs of switching to low carbon energy and business as usual.