Transformer Calculator
Calculate transformer turns ratio, voltage, and current from primary and secondary specifications.
Calculator
Adjust values & calculateTransformer Summary
Formula
Where Vp and Vs are primary and secondary voltages, Np and Ns are primary and secondary turns, and Ip and Is are primary and secondary currents. For an ideal transformer, power in equals power out: Vp x Ip = Vs x Is.
Last reviewed: December 2025
Worked Examples
Example 1: Residential Step-Down Transformer
Example 2: Industrial Step-Up Transformer
Background & Theory
The Transformer Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ the permanent self-weight of structural elements, finishes, and fixed equipment โ and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ0.45 typically yields concrete with 28-day compressive strengths of 30โ40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ350 MPa for mild steel) and ultimate tensile strength (typically 400โ500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.
History
The history behind the Transformer Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ a mixture of volcanic ash, lime, and seawater โ enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ including the 1971 San Fernando and 1994 Northridge events โ drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.
Frequently Asked Questions
Formula
Vp/Vs = Np/Ns = Is/Ip
Where Vp and Vs are primary and secondary voltages, Np and Ns are primary and secondary turns, and Ip and Is are primary and secondary currents. For an ideal transformer, power in equals power out: Vp x Ip = Vs x Is.
Worked Examples
Example 1: Residential Step-Down Transformer
Problem: A transformer has 500 primary turns at 240V and needs to output 120V with a 1000W load at 95% efficiency. Calculate secondary turns, currents, and losses.
Solution: Turns Ratio = 240 / 120 = 2:1\nSecondary Turns = 500 / 2 = 250 turns\nSecondary Current = 1000 / 120 = 8.333A\nIdeal Primary Current = 1000 / 240 = 4.167A\nInput Power = 1000 / 0.95 = 1052.63W\nActual Primary Current = 1052.63 / 240 = 4.386A\nPower Loss = 1052.63 - 1000 = 52.63W
Result: Turns: 2:1 (500:250) | Primary: 4.386A | Secondary: 8.333A | Loss: 52.63W
Example 2: Industrial Step-Up Transformer
Problem: A step-up transformer converts 120V to 480V with 200 primary turns and a 5000W load at 97% efficiency.
Solution: Turns Ratio = 120 / 480 = 0.25:1 (step-up)\nSecondary Turns = 200 / 0.25 = 800 turns\nSecondary Current = 5000 / 480 = 10.417A\nInput Power = 5000 / 0.97 = 5154.64W\nActual Primary Current = 5154.64 / 120 = 42.955A\nPower Loss = 5154.64 - 5000 = 154.64W\nImpedance Ratio = 0.25^2 = 0.0625
Result: Turns: 0.25:1 (200:800) | Primary: 42.96A | Secondary: 10.42A | Loss: 154.64W
Frequently Asked Questions
How does a transformer work and what is the turns ratio?
A transformer works on the principle of electromagnetic induction, transferring electrical energy between two or more windings through a shared magnetic core. The turns ratio is the ratio of the number of turns in the primary winding to the number of turns in the secondary winding, expressed as Np divided by Ns. This ratio directly determines the voltage transformation relationship, where Vp divided by Vs equals Np divided by Ns. A transformer with 1000 primary turns and 500 secondary turns has a turns ratio of 2 to 1, meaning it steps down the voltage by half. The turns ratio is the most fundamental parameter in transformer design and determines whether the transformer steps voltage up or down.
How do you calculate transformer efficiency and power losses?
Transformer efficiency is calculated as the ratio of output power to input power, expressed as a percentage using the formula Efficiency equals output power divided by input power times 100. Power losses in transformers come from two main sources: copper losses and core losses. Copper losses, also called I-squared-R losses, occur due to the resistance of the winding conductors and increase with the square of the current. Core losses include hysteresis losses from the continuous magnetization and demagnetization of the core material and eddy current losses from circulating currents induced in the core. Modern power transformers typically achieve efficiencies of 95 to 99 percent. Distribution transformers are usually rated at 97 to 99 percent efficiency at full load.
What is impedance ratio and why is it important in transformer design?
The impedance ratio of a transformer equals the square of the turns ratio, expressed as the quantity Np divided by Ns, all squared. This relationship is crucial for impedance matching in electronic circuits, particularly in audio equipment and RF applications. For example, a transformer with a 10 to 1 turns ratio has an impedance ratio of 100 to 1, meaning a 100 ohm load on the secondary appears as a 10,000 ohm impedance on the primary side. Maximum power transfer occurs when the source impedance matches the load impedance. Audio output transformers use this principle to match the high impedance of vacuum tube amplifiers to the low impedance of speakers, ensuring efficient power delivery.
How do you size a transformer for a specific application?
Sizing a transformer requires determining the VA (volt-ampere) rating, which is calculated by multiplying the secondary voltage by the maximum secondary current. For resistive loads, VA equals watts, but for inductive or capacitive loads you must account for the power factor. A motor drawing 10 amps at 120 volts with a power factor of 0.8 requires 1200 VA but only consumes 960 watts. Always add a safety margin of 20 to 25 percent above the calculated VA rating to prevent overheating and ensure reliable operation. Consider ambient temperature conditions since transformers derate at higher temperatures. For applications with significant inrush current like motors, size the transformer to handle the starting current, which can be 5 to 8 times the running current.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I verify Transformer Calculator's result independently?
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
References
Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy