# Displacement to Torque Calculator, Formula, D to T Calculation

## Displacement to Torque Calculator:

Enter the values of work done, W(J), radius, r(m) and displacement, d­(m) to determine the value of displacement to torque, T(N.m).

 Enter Workdone: J Enter Radius: m Enter Displacement: m Result – Displacement to Torque: N.m

## Displacement to Torque Calculator:

Displacement to torque refers to the conversion of linear force applied over a distance (displacement) into rotational force (torque) around a pivot point.

Displacement to torque, T(N.m) in Newton metres is equated by dividing the product of work done, W(J) in joules and radius, r(m) in metres by displacement, d­(m) in metres.

Displacement to torque, T(N.m) = W(J) * r(m) / d­(m)

T(N.m) = displacement to torque in Newton metres, N.m.

W(J) = workdone in joules, J.

r(m) = radius in metres, m.

(m) = displacement in metres, m.

## Displacement to Torque Calculation:

1. If a force of 100 N is applied to move an object 2 metres, and this force is applied at the end of a lever 0.5 metres long, calculate the torque produced at the pivot point of the lever.

Given: F(N) = 100N, d­(m) = 2m, r(m) = 0.5m.

First, calculate the work done: W(J) = F(N) * d­(m)  = 100 * 2 = 200J

Displacement to torque, T(N.m) = W(J) * r(m) / d­(m)

T(N.m) =  200 * 0.5 / 2

T(N.m) = 50N.m.

2. Consider a scenario where 500 Joules of work is required to move a gate. The displacement of the handle along its arc is 3 meters and the torque applied at the hinge to move the gate is 166.67N.m. Determine the force is applied via a handle away from the hinge (pivot point).

Given: W(J) = 500J, d­(m) = 3m, T(N.m) = 166.67N.m.

Displacement to torque, T(N.m) = W(J) * r(m) / d­(m)

r(m) = T(N.m) * d­(m) / W(J)

r(m) = 166.67 * 3 / 500

r(m) = 1m.