In this paper we analyze the power consumption and energy efficiency of general matrix-matrix multiplication (GEMM) and Fast Fourier Transform (FFT) implemented as streaming applications for an FPGA-based coprocessor card. The power consumption is measured with internal voltage sensors and the power draw is broken down onto the systems components in order to classify the energy consumed by the processor cores, the memory, the I/O links and the FPGA card. We present an abstract model that allows for estimating the power consumption of FPGA accelerators on the system level and validate the model using the measured kernels. The performance and energy consumption is compared against optimized multi-threaded software running on the POWER7 host CPUs. Our experimental results show that the accelerator can improve the energy efficiency by an order of magnitude when the computations can be undertaken in a fixed point format. Using floating point data, the gain in energy-efficiency was measured as up to 30 % for the double precision GEMM accelerator and up to 5 × for a 1k complex FFT.