Businesses plan an increase in real capital spending for plant and equipment this year that will be double the rate of increase for 1976, the Commerce Department said yesterday.

The department said business project expenditures for capital improvements and expansion that would total about 6 per cent after accounting for inflation. Real capital investment in 1976 increased about 3 per cent over 1975.

The rise in spending for plant and equipment would lead to more production, higher productivity and increased hiring in 1977. Capital expenditures are the basis for economic growth.

The forecast is based on the department's annual survey of businesses conducted in November and December. The picture emerging from the latest annual survey is more optimistic than that portrayed in the most recent quarterly survey by the department, which showed little increase in spending during the first six months of 1977. The annual survey doesn't indicate when in a given year expenditures are expected to take place.

"Businesses were concerned about inflation and the strength of the economic recovery in late 1975 and early 1976," a COmmerce Department spokesman said. "Inflation is abating and the economy is growing again, which was encouraging for management in making assessments for 1977."

Commerce said business expects to spend $135 billion for new plant and equipment, 11.3 per cent more than the estimated $121.2 billion spent in 1976. In prices of capital goods increase at the 1976 rate of 5 per cent, the increase after accounting for inflation would be about 6 per cent, the department said.

However, the department noted that businesses had estimated the price increase for capital goods in 1976 at 8 per cent and had said they anticipate a similar increase in prices this year, indicating a smaller rise in real investment.

Commerce said capital spending rose by 7.5 per cent last year to $121.2 billion. After adjustment for inflation by means of the implicit price deflator for fixed nonresidential investment, the increase was in the range of 3 per cent.

Industry by industry, the biggest jump in spending was expected in motor vehicles, which showed an expected increase of 38.3 per cent to $3.4 billion. Capital spending in that sector had climbed 20.3 per cent last year.

Big increases also were expected in air transportation, up 26.1 per cent to $1.7 billion after a 27.9 cent decrease last year; a 11.6 per cent rise to $1.1 billion in the aircraft industry; a 27.4 per cent rise in the rubber industry to $1.4 billion; a 16 per cent rise in the paper industry to $4 billion; and a 14.1 per cent increase to $25.6 billion among public utilities.

Other industries signalling increases of 10 per cent or more included electrical and other machinery, textiles, petroleum, mining, railroads and communications.

The estimates are subject to fluctuation as business plans firm up and leaders get a better look at the economy. But the November-December survey in 1975 was off only slightly from actual spending.

Capital spending of $121.2 billion compared to an estimate of $119.7 billion published at this time last year.